mersenneforum.org - Aliquot sequences that start on the integer powers n^i

mersenneforum.org (https://www.mersenneforum.org/index.php)

- Aliquot Sequences (https://www.mersenneforum.org/forumdisplay.php?f=90)

- - Aliquot sequences that start on the integer powers n^i (https://www.mersenneforum.org/showthread.php?t=23612)

I have now finished running WGET's on all ELF's for bases > 3000. It works like a charm. All of the sequences are now rebuilt and pull up very quickly. My process is touching all sequences, both open and terminated.

It's easy to tell that the sequences have been rebuilt. Not only do they come up quickly, they no longer have the "Checked, new" under the status for each index.

Jean-Luc, I think you can do a quick update on your pages for all bases > 3000 at this moment.

I was able to run specifically bases 8128 thru 30030 (12 bases/480 sequences) in one big batch. It took 32 minutes to run. I didn't have any hiccups. I'll keep gradually increasing the batch size.

I'll see how far I can get with this before signing off. I'm going to shoot for all bases > 300. Then later on Monday I'll see how many more I can do while gradually increasing the batch size.

I've started my local set update as well. You'll probably notice a change as we meet somewhere, but your efforts will be more complete than mine since you are also including terminated sequences.

I'm now down under base 800. The large # of double-square bases just above that made it run much more quickly in that area.

I will stop at base 300 for the morning and then do some more starting early evening.

Hopefully after we are done with all of this, Jean-Luc can do all his updates in one setting.

My efforts have totally stalled and I'm quite stuck for at least another half-hour. I may have to abandon my update effort for now. It had only made it part way into the base 3 set.:sad:

I have completed accessing all sequences for bases > 300 using wget. I spot-checked many of the longest sequences to verify that they pulled up quickly. All sequences appear to have been rebuilt.

Jean-Luc, it is my hope that you can quickly run updates for all bases > 300 at this time. :smile:

I will continue with this later today.

I just got home from work and read your posts.
I think you are right.
I hadn't thought of downloading the .elf's to force the reconstruction of the sequences.
I will do some work in this direction soon so that I can do this myself after the next maintenance operation on FactorDB.
Thank you for helping me in this way.
I will try to make progress with the updates during the week, but it is not easy when I am working.
I will start with the bases >300, it will be a good step done.
For the smaller bases, I'll see later.

I tried my update script and it quickly overran the limits twice, without making it through the base 3 table. Apparently just grabbing an .elf is less taxing than checking a last line.

I believe I just verified that as the case. I'll have to rewrite my scripts to stop checking whether work was done and just d/l the current .elf.

I've modified my update scripts and I'll see how they proceed. So far I've used very little of my allocation for factordb. Let's hope that continues. If all works as hoped I'll cover the smaller tables by this evening.

Ed, I hope that is working out for you. Anything to speed up the updating processes is a plus!

Meanwhile, I am starting my ELF grabbing again here shortly. I ran down to base 288 this morning. I'll start now with bases 240-285, then bases 200-240, etc. For now I'm splitting them up where there is a change in the number of exponents in each base. Down to base 100, it's a good dividing line for slowly increasing the number of sequences I do each time.

My interim goal will be to get down to base 70 by early morning. I'll keep everyone updated.

My update script is working. The good news is that it is using next to nothing toward the db limits. The bad news is that it is extremely slow. From when I started it around 8 hours ago, it has only completed through base 42. And, if it's working correctly, only open sequences in my local set are run, so you should still continue your march all the way through base 2. My run, if all goes well will be through the topmost base we have.

All sequences for all bases > 100 in the DB have now been rebuilt. The process is continuing.

I should be able to complete everything tonight and early morning.

With my scripts (which uses Garambois, too) I can process ~30 bases at once before the FactorDB limit for one hour is reached by now.

1) ~1.2M Database queries allowed in an one hour period by FactorDB
2) ~30k-50k Database queries for one base with ~40%-50% open seqs
3) to read the last line of a seq, you need a little bit more Database queries than indices exists

At a total of 201 bases (better 192 because 9 are without any open seq so far) for this project it takes ~6-7 hours to process all bases.
Perhaps a little faster, because ~80 bases got <40 open seqs, but only 16 got >60 open seqs.

PS: Currently my data holds only 138 bases so far and there're ~4,2 M indices overall from open seqs.

All sequences for all bases > 50 have now been rebuilt. Continuing...

Ed, I can see that somewhere around the 60s, 70s, or 80s, I intersected with you and all of the open sequences were already rebuilt. I am continuing accessing all of them just in case but the process now only appears to hesitate on the terminated sequences with many iterations. That means I'll have fun on base 2. :-)

My update completed fully in about 12.5 hours, so it must have sped up once it reached the edge of those already touched. But there were some unexpected error messages for the new bases. I don't think there were errors in the retrieval, but I'm reworking them now. Oddly, even though I am retrieving the whole .elf now, the db limit values are not showing any increase. Perhaps retrieving .elfs is no longer a problem once they're built. I'll do that now instead of trying to compare first. That should mean I can go back to full local set updates without db limit worries.

[QUOTE=kar_bon;614289]With my scripts (which uses Garambois, too) I can process ~30 bases at once before the FactorDB limit for one hour is reached by now.
[/QUOTE]
This is also the case for me once the sequences are reconstructed.
But when they are not rebuilt, it sometimes takes me 2 or even 3 hours for a single base.
But I think this is independent of the scripts and only depends on FactorDB.

Otherwise, I just tried some random databases : yes it seems that everything works normally again.
I'll start doing some updates, but since it's the middle of the week, I don't have much time and I certainly won't do all the work.

Many thanks to all for your help !

All sequences for all bases >= 10 have been rebuilt. I'll submit one final batch process to complete bases 2 thru 7 within a few minutes. That will complete the process.

Ed's process rebuilt all of the open sequences. So the only thing remaining to rebuild is terminated sequences for bases 2 thru 7, which I am about to take care of.

I also took care of the 4 new bases listed under "tables being initialized" on the main page.

So you are good to go! :-)

A small update on my recent progress after Sep.14:

The updated sequences are 233^4,233^8,233^16,233^24,233^28,233^48,(and 233^67)

Detailed information for these exponents are attached (but probably useless)

I'm currently doing some benchmark using the C140 and C148 from 233^67.

Sequence 233^67 should probably terminate after 3 days on my machine.

After that I will get back to (previously reserved) opposite base work for base 233.

I have extended 99^44, 157^32, 157^34, 157^36, 293^36, 293^38, and 293^40 to > 110 digits.

The first 5 of these sequences were not previously tested to 100 digits.

I think that all unreserved opposite-parities on the project now are at >= 100 digits.

Yoyo terminated 55^76! :-)

In other news:
52^39 is a merge but the merge info. is not shown on the page.

It merges at index=1221 with 27450:i52.

By the way, I do not have a merge tool. I am doing the merge info. by eye by looking on the blue page. I like solving the puzzle. Without the blue page or a merge tool, it would be next to impossible. Regardless, it's best to check me.

Verified:[code]Running base 52:
52^5:i33 merges with 5208:i6
52^37:i369 merges with 7044:i129
52^39:i1221 merges with 27450:i52
52^41:i604 merges with 2712:i10[/code]

99^6 was advanced to 115 digits.

I did a final detailed check of all of the pages looking for unreserved sequences having not been tested to 100 digits. I found this one final one that was previously at 98/91. Now I think everything is at >=100 digits.

Reserving 14^61 to ~125 digits.

This is a strange one that I found while doing the above. It was at 112/98. (I've now advanced it to 116 digits.) All of the smaller bases had been advanced long ago by Yoyo and others to >= 140 digits. This one reached 142 at one point, dropped to 83, and then was moved back to 112. My guess is that Yoyo released it at 140-142 somewhere but someone else happened to catch the down-driver shortly after that. Once it was lost, it was a lot of work to move it back to where it was.

Perhaps Yoyo or someone else can take it again after I'm done and bring it back to 140 digits so it doesn't stand out from the crowd. :-)

The page has been completely updated, thanks to Karsten's new scripts, very quick to implement.
Thank you all for your help.
I had 6 FactorDB interruptions to make this complete update, with the sequences already built.
I hope I have not forgotten anything, please check.

[B]Added base : 828[/B]

Karsten's scripts give the sequences below as being at index 1 :
[CODE] 102 81 164 130
102 83 168 154
102 85 172 165
102 86 174 162
102 92 186 183
102 93 188 167
104 79 160 159
104 90 182 134
104 91 184 145
104 94 190 155
104 95 192 162
105 68 138 135
105 81 164 160
105 86 174 174
105 90 182 156
105 91 185 142
105 92 187 149
105 93 189 179
105 94 191 162
105 95 193 147
1058 53 161 145
1152 51 157 152
1155 51 157 148
119 80 166 157
119 88 183 166
119 94 195 181
120 69 144 134
120 73 153 149
120 80 167 163
120 83 174 163
120 84 176 149
120 85 178 158
120 87 182 145
120 90 188 166
120 91 190 153
120 95 198 182
12496 37 152 148
1352 52 163 154
137 89 189 145
14264 40 167 159
14288 39 163 145
14316 39 163 148
14316 40 167 152
15015 38 159 146
162 83 184 132
162 85 189 183
162 86 191 156
162 87 193 166
162 89 197 167
162 90 200 184
173 83 184 162
18 135 170 164
193 83 188 176
20 122 159 150
20 124 162 145
200 73 169 159
200 75 173 156
200 77 178 154
200 78 180 145
210 61 143 133
210 66 154 143
210 69 161 131
210 73 171 150
210 77 180 147
210 78 182 179
22 123 166 149
220 75 176 166
220 78 183 143
220 80 188 170
229 79 185 181
231 65 154 142
231 67 159 150
231 69 164 160
231 76 180 164
24 111 154 149
24 119 165 143
24 120 166 151
24 121 168 130
24 125 173 135
26 116 165 157
26 119 169 149
26 120 170 154
276 59 145 142
276 61 150 133
276 64 157 149
276 65 159 154
276 67 164 147
276 69 169 157
28 113 164 157
28 114 166 150
28 116 168 152
284 69 170 150
30 110 163 150
30 119 177 134
30 120 178 156
31704 35 158 141
31704 38 172 171
31704 39 176 153
33 98 149 147
33 105 160 134
33 106 161 150
33 109 166 143
34 104 160 154
34 107 164 161
35 98 151 150
38 104 165 144
385 62 161 142
39 99 158 152
39 106 169 160
392 64 167 159
392 65 169 166
396 62 162 155
40 98 158 146
40 103 166 146
40 106 170 150
40 107 172 152
45 98 162 145
46 96 160 148
46 97 162 146
48 96 162 135
51 92 157 148
52 91 157 151
52 95 164 145
54 99 172 163
55 94 164 150
552 59 163 147
56 91 160 153
56 97 170 150
56 98 172 154
57 95 167 161
57 100 176 154
60 87 156 149
60 96 172 163
60 100 179 151
62 89 160 154
62 92 165 151
62 96 173 158
63 97 175 150
63 98 177 130
6469693230 16 158 156
6469693230 18 178 166
65 89 161 155
65 98 178 153
66 93 170 132
660 53 150 128
660 55 156 142
68 92 169 161
68 97 178 170
68 99 182 157
68 100 184 170
69 90 166 134
69 91 168 151
69 97 179 177
696 54 154 144
696 56 160 135
696 59 169 160
696 60 171 152
70 81 150 149
70 89 165 162
72 91 170 137
72 98 183 178
720 49 141 134
74 85 159 147
74 89 167 132
74 90 169 151
74 91 171 135
74 97 182 169
74 98 184 178
75 86 162 154
75 92 173 156
75 96 180 153
76 85 160 154
76 95 179 173
76 97 183 141
76 98 185 146
77 80 151 145
77 89 168 163
77 90 170 156
77 97 183 175
78 89 169 161
78 91 173 167
78 94 179 171
78 96 182 166
78 97 184 170
78 98 186 184
78 99 188 176
780 53 154 145
780 58 169 162
780 60 175 149
80 88 168 151
80 92 176 159
80 95 181 152
80 96 183 143
82 93 179 151
82 97 186 146
82 98 188 155
828 55 161 143
828 56 164 146
84 83 161 149
84 89 172 162
84 92 178 132
84 94 182 178
84 100 193 158
85 82 158 154
85 85 164 134
85 96 185 158
85 99 191 135
8589869056 19 189 162
8589869056 20 199 168
86 77 149 142
86 80 155 150
86 87 169 131
86 90 175 132
86 95 184 178
86 96 186 166
86 98 190 160
86 99 192 189
87 76 148 142
87 83 161 153
87 94 183 160
87 95 184 147
87 96 186 176
87 99 192 142
87 100 194 173
88 93 181 149
88 95 185 167
88 96 187 158
88 97 189 131
882 55 163 156
882 57 169 141
882 59 175 168
90 89 175 172
90 92 181 160
90 93 183 149
90 95 187 163
90 96 189 132
91 91 178 169
91 93 182 153
91 95 186 165
91 96 188 163
91 97 190 175
92 86 169 149
92 94 185 174
92 95 187 170
92 97 191 182
92 98 193 155
92 99 195 151
93 82 162 158
93 86 170 149
93 93 183 162
93 96 189 157
93 99 195 154
94 83 164 157
94 84 166 150
94 91 180 172
94 92 182 170
94 96 190 167
94 97 192 164
94 99 196 164
94 100 198 156
95 76 150 146
95 78 154 151
95 90 178 153
95 94 186 186
95 96 190 175
95 99 196 180
96 77 153 146
96 81 161 153
96 84 167 155
96 86 171 166
96 94 187 181
96 97 193 180
96 98 195 170
96 99 197 179
96 100 199 149
966 52 156 149
966 54 162 153
966 59 177 166
98 98 196 179
99 78 156 131
99 82 164 153
99 86 172 170
99 92 184 134
99 94 188 157
99 98 196 178
99 99 198 181
[/CODE]

Hmm, I seem to have a few more in my list and three in your list have since moved past index 1.. I'll do some more comparison. It may be because I've included all the pending bases as well. I'd rather have a couple extra than miss some.

Thanks for all the updating. I'll update both of the other threads later today.

[QUOTE=EdH;614457]Thanks for all the updating. I'll update both of the other threads later today.[/QUOTE]

Please forgive me for this. But take responsibility for the listening.

Normal is something to get away from. Serioously.

[QUOTE=EdH;614457]Hmm, I seem to have a few more in my list and three in your list have since moved past index 1.. I'll do some more comparison. It may be because I've included all the pending bases as well. I'd rather have a couple extra than miss some.

Thanks for all the updating. I'll update both of the other threads later today.[/QUOTE]
When I did the initial compare of Jean-Luc's vs. your list both shown in the index 1 thread, yours had the pending bases whereas his did not. When I added back those to his list and then removed what we had since moved past index 1, they matched. Hopefully that is what you will find.

'Tis true. My list includes 882, 888, 996 and 1264460. Otherwise, all matches. It's good to check with a couple sources, though.

[QUOTE=EdH;614467]'Tis true. My list includes 882, 888, 996 and 1264460. Otherwise, all matches. It's good to check with a couple sources, though.[/QUOTE]

So... I currently have a few people saying to me "what the fsck are you doing...

[URL="https://www.youtube.com/watch?v=dLxpNiF0YKs"]Man on the Moon[/URL]. It can be useful being insane!

Thanks for the ton of updates Jean-Luc!

Releasing 14^61 at 125/122 full ECM. It went up quickly and so took less time than I expected. Hopefully Yoyo or someone will take it back to 140 digits in the near future.

[QUOTE=chalsall;614472]So... I currently have a few people saying to me "what the fsck are you doing...

[URL="https://www.youtube.com/watch?v=dLxpNiF0YKs"]Man on the Moon[/URL]. It can be useful being insane![/QUOTE]

I think you spelled "inane" incorrectly.

@chalsall :
I'm really sorry, but not being an English speaker, I don't understand the purpose of your posts, because I use machine translation and I don't know enough English.
I don't understand what you mean.
Please, could you explain your requests or demands ?
Thank you.

[QUOTE=garambois;614526]@chalsall :
I'm really sorry, but not being an English speaker, I don't understand the purpose of your posts, because I use machine translation and I don't know enough English.
I don't understand what you mean.
Please, could you explain your requests or demands ?
Thank you.[/QUOTE]

It's not a language issue. I'm a native speaker, and even I'm lost.

[QUOTE=garambois;614526]@chalsall :
I'm really sorry, but not being an English speaker, I don't understand the purpose of your posts, [/QUOTE]

user chalsall likes to drop in on threads with topics he is not especially conversant, either to give an oddly worded "thumbs up" or "good job" with no context, or he composes some vague parallel to his experience in coding or network administration. If you cannot make sense of his posts, chances are high it's one of these two categories and can be ignored.

Unfortunately, asking him what he's on about often leads to some sort of confrontation- he thinks it's a game, sometimes to the point of receiving a temporary ban from the forum. If you pretend he's talking to himself when he's not a central part of the thread conversation, you're likely to have the right idea.

@Happy and Curtis :
Thank you for your explanations !

[QUOTE=VBCurtis;614534]....[/QUOTE]
:lol:

[QUOTE=SuikaPredator;614329]A small update on my recent progress after Sep.14:

The updated sequences are 233^4,233^8,233^16,233^24,233^28,233^48,(and 233^67)

Detailed information for these exponents are attached (but probably useless)

I'm currently doing some benchmark using the C140 and C148 from 233^67.

Sequence 233^67 should probably terminate after 3 days on my machine.

After that I will get back to (previously reserved) opposite parity work for base 233.[/QUOTE]

233^67 terminated, back to work:cool:

A couple of notes (probably to Karsten) about the main data page HTML syntax:[list=1][*]The angle bracket in "term <145 digits" needs to be escaped as [c]<[/c].[*]There are duplicate closing tags at the end of line 115 (the merged sequence example).[/list]

I'm starting another run of initializations. Bases 353 and 359 can be added at the next update.

[url='http://factordb.com/sequences.php?se=1&aq=65^66&action=last20']65^66[/url] terminates in the amicable pair (635624,712216) after ~1300 more lines.

Excellent! Another cycle found!

Wow !
And on top of that, the cycle is not ordinary !

All of base 24 is now >= 120 digits.

Work on odd exponents 67 to 83 finished it off.

Bases 367 and 373 can be added at the next update.

367^44 terminated by me. :-)

Page updated, but not all bases.
A complete update will be done between October 22 and 29.
Thank you very much to all for your work.
Do not hesitate to point out any error.

[B]Added bases : 353, 359, 367, 373, 888, 1264460.[/B]
[B]Some reservations, attributions added according to the last thread messages.[/B]

Wow! That totally cleared out the "Somewhat Easier" thread. Thanks for all the work.

Excellent on the updates! Don't forget to update bases 14 and 24 on the next update. All opposite sequences are now orange or pink! :-)

On the main page, new base 1264460 is not factored in the decomposition column.

Reserving 20^101,103,105

Bases 379 and 383 can be added at the next update.

Page updated.
Many thanks to all for your work !

[B]Added bases : 379, 383, 996.[/B]
[B]Some bases updated and corrections made according to the requests on the project thread.[/B]

The project now has over 10,000 terminated sequences !
As a good Frenchman, I'll probably open the Champagne tonight, even if we are still far from the weekend !
Or maybe a good Bavarian weissbier as I like them, living on the German border.

:smile:

[QUOTE=gd_barnes;614479]Thanks for the ton of updates Jean-Luc!

Releasing 14^61 at 125/122 full ECM. It went up quickly and so took less time than I expected. Hopefully Yoyo or someone will take it back to 140 digits in the near future.[/QUOTE]

[QUOTE=gd_barnes;614985]All of base 24 is now >= 120 digits.

Work on odd exponents 67 to 83 finished it off.[/QUOTE]

[QUOTE=gd_barnes;615211]Excellent on the updates! Don't forget to update bases 14 and 24 on the next update. All opposite sequences are now orange or pink! :-)[/QUOTE]

Still waiting for these updates. I think it's been two updates since I completed the work. :-)

Bases 70 to 79 have now had their large opposite-parity exponents initialized.

Also included in this initialization were new bases 353, 359, 367, 373, 373, 379, 383, 888, and 1264460. Out of all of these new bases, I think that only base 1264460 still needs to be updated.

I'm sorry, but I really don't have time to do a full update right now.
I shouldn't have even made this update today !

But as I had said above, I will do that in 10 days, it will be better for me.
Because I will have to do a clean job and check several things.

;-)

Thanks for all your work, Jean-Luc! You cleared most of the other thread's current terminations and now I can remove some bases from my scripts. That should allow them to update a little faster.

[QUOTE=garambois;615455]I'm sorry, but I really don't have time to do a full update right now.
I shouldn't have even made this update today !

But as I had said above, I will do that in 10 days, it will be better for me.
Because I will have to do a clean job and check several things.

;-)[/QUOTE]
Ah OK. I thought you had just missed those. Thanks for all of the updates! :smile:

Bases 389 and 397 can be added at the next update.

397^46 terminated by me.

Page updated.
Many thanks to all for your work !

[B]Added bases : 389, 397.[/B]
[B]Some bases updated according to what was requested in the project thread from post #1992.
[/B][B]But I haven't checked anything due to time constraints, I hope everything is OK ![/B]

Of course, as I had announced, within a week, I will make a very complete update of the page.

Bases 50 to 69 have now had their large opposite-parity exponents initialized.

Also included in this initialization were new bases 389, 397, and 996.

Reserving new base 40320. I'd like to extend the factorial bases and I see that base 5040 is being worked on.

Jean-Luc, can I assume that exponent 35 will be the highest exponent shown for this base on your page? 40320^35 is 162 digits.

I'm asking because it falls between bases 31704 and 131071, which have exponents up to 40 and 35 respectively shown on your page.

[QUOTE=gd_barnes;615768]
Jean-Luc, can I assume that exponent 35 will be the highest exponent shown for this base on your page? 40320^35 is 162 digits.
[/QUOTE]
As you are the first to initialize this base, you have the privilege to choose the limit exponent !
35 is fine if you decide to do so.
I might have placed the exponent change from 40 to 35 from base 50,000 myself, but 40320^38 has the 3 in its factors, which makes it a terrible sequence !
As for 40320^40, with cofactors over 180 digits long, that scares the hell out of me.

[QUOTE=garambois;615774]As you are the first to initialize this base, you have the privilege to choose the limit exponent !
35 is fine if you decide to do so.
I might have placed the exponent change from 40 to 35 from base 50,000 myself, but 40320^38 has the 3 in its factors, which makes it a terrible sequence !
As for 40320^40, with cofactors over 180 digits long, that scares the hell out of me.[/QUOTE]
I will certainly choose exponent 35 for the limit. Perhaps the exponent change from 40 to 35 can begin at base 40000. :-)

OK Gary, excellent !
A lot of thanks !

Base 40320 is complete to exponent 35 and can be added at the next update.

Merges:
40320^3 merges at index=892 with 10212:i369
40320^5 merges at index=211 with 39060:i16
40320^11 merges at index=1181 with 660:i25

I've rewritten my scripts to do a total update of all my local set of sequences based entirely on the tables and using .elf downloads. I no longer have to manually tell the scripts to add tables and I no longer show use of factordb resources. I was surprised to find that over 1000 sequences were either updated or added since my last update. This one took just about 8 hours to complete and I didn't have to watch the limits.

There was a catch I needed to take into account, though. As has been discussed before, several of the larger sequences, the ones above 200 digits, bring in an empty .elf from factordb. In these cases, I have elected to have a correct .elf in my local set (although not all have been completed yet). I needed to keep in mind not letting the empty .elf overwrite the valid one.

Great work to avoid those limits!

I have continued my large opposite-parity initialization on down below base 50 where it stood on my last status. Currently I just passed base 20 on my way down. It should be complete for all bases within ~1-2 days. It's quick for the smaller bases because there are almost no sequences at < 140 digits. This has the effect of adding just a few indexes or even a lone factor or two to a lot of sequences. That's part of the reason you have over 1000 changes. That plus the very large number of new bases recently.

I wonder if the FactorDB admin would entertain the notion of fixing the elfs for > 200 digits. Perhaps make the limit 250 digits or something like that.

I ran across something odd in my local files today! I wrote a script to verify (with Aliqueit) every .elf I have locally stored. It told me I have 18512 individual .elfs. But what was odd, was that it also told me that 2^236 had a composite number in the index 1 factors list. This was true, but all the subsequent indices were OK when I re-verified the .elf.

[QUOTE=EdH;615958]But what was odd, was that it also told me that 2^236 had a composite number in the index 1 factors list. This was true, but all the subsequent indices were OK when I re-verified the .elf.[/QUOTE]
Please Edwin, can you tell us what this composite factor is, because I couldn't find it ?
All factors given by the .elf for the sequence 2^236 at index 1 are prime !
Or have I misunderstood ?

The factordb .elf is correct and mine is now, as well. But, it is good you checked yours. In my case, there was a composite consisting of two of the prime factors and those two primes were not listed. I expanded the composite into the primes and removed the composite and all was well. My local copy was from quite some time ago and was not touched in any of my updates due to it being terminated. (I check for termination before retrieving an .elf.) However, when I ran Aliqueit against all the .elfs, it turned up this error. Perhaps the error existed way back when I downloaded the original terminated .elf, but has since been corrected by one of the db rebuilds. In any case, I guess it's good to verify the .elfs every once in a while.

For further details, this is the correct index 1:[code]1 . 110427941548649020598956093796432407239217743554726184882600387580788735 = 3 * 5 * 1181 * 2833 * 3541 * 37171 * [B]157649 * 174877[/B] * 179951 * 5521693 * 1824726041 * 104399276341 * 3203431780337[/code]This was the invalid one:[code]1 . 110427941548649020598956093796432407239217743554726184882600387580788735 = 3 * 5 * 1181 * 2833 * 3541 * 37171 * 179951 * 5521693 * 1824726041 * [B]27569184173 [/B]* 104399276341 * 3203431780337[/code]What confused me most was index 2 being correct. Wouldn't it have had to have been made from the correct primes?

OK Edwin, thank you for these explanations.
This is all very strange !

This doesn't strike me as strange. Since I manually enter all of my indexes, on the newest index that it builds itself (that I have not entered) the FactorDB will often have a 10 to 20-digit composite factor that it takes several minutes before it factors it (in addition to the big 100+ digit regular composite). My guess is that it is either waiting for the factoring "elves" to get to it or (if under 19 digits) is waiting for its own process to factor it.

This is likely due to the DB being bogged down at the moment. I believe the DB knows not to create a subsequent index if the current one contains a composite factor.

My guess is that you picked up your elf in that interim period when the small composite wasn't factored. Although quite a bit more rare, I've even seen it show a composite 8 or 9-digit factor for over a minute that it eventually finds to have a 1-digit prime factor of 3, 5, or 7. It's weird.

But, why would the subsequent lines even exist if it hasn't correctly written a current one?

[QUOTE=EdH;616038]But, why would the subsequent lines even exist if it hasn't correctly written a current one?[/QUOTE]

It could be that the elf was wrong for a period of time in the FactorDB. But that strikes me as odd because I feel like the elf is rebuilt each time it is downloaded. In other words, it would not "remember" any previous times that elfs were downloaded for a specific sequence.

Other than that, the only thing I can think is that you downloaded it at different times, one before the number was completely factored and one after. I assume that you process probably overlays anything that's currently there. But if that is not the case, could your process have concatenated a newly terminated sequence onto the back end of the previous partially completed one beginning with the index right after the previous one?

2^236 was done before I started working with this project, so I would have just downloaded the already existent .elf. The db must have cosidered the composite as a prime at the time, but that wouldn't account for the next index being correct. Oh, well, it's all OK now.

Bases < 50 have now had their large opposite-parity exponents initialized.

This completes this effort. All unreserved sequences on the project of both parities for all sizes have now had at least some work done on them.

[QUOTE=EdH;616072]2^236 was done before I started working with this project, so I would have just downloaded the already existent .elf. The db must have cosidered the composite as a prime at the time, but that wouldn't account for the next index being correct. Oh, well, it's all OK now.[/QUOTE]
I take back what I said earlier. That strikes me as VERY strange! I wonder if it was one that was wrong in the FactorDB for a while before it finally got noticed and corrected. But if that was the case, you would have had an elf that was wrong for subsequent indexes too. That is so weird.

Weird stuff like this happens on the No Prime Left Behind stats SQL database sometimes when I have a power blip in the middle of our automated hourly update. Strange results/residues will end up in our results DB that mess up the stats. I have to manually go in and remove the mess. I wonder if it could have been something like that since the FactorDB has had a few power blips. Programs can act really badly when they are interrupted unexpectedly.

Nice to visit those pages after a while and see the progress you all did here! Congratulations!

Now, I did that because some people (hi Gary! :razz:) are kicking my back on PM about the reservations for base 28. I thought base 28 is done (by me!) long time ago, as well as base 6 (of which I wrestled in the past, partially). Most of those should be at 150 or more digits. Do you want to extend them? Be my guest(s). I didn't do any work for those in years, and if anybody needs to extend them, please consider them unreserved from my side. Please note that all the mergers (IIRC, one with base 28 and 3 or 4 with base 6) are still reserved by me on the main aliquot project, and I [U]DO[/U] work them regularly (see the blue page), so leave them alone. The rest, like RDS would say, fell free to have at it.

Long story short: LaurV is releasing base 28 except for the merged sequences that he's working on in the main project. :smile:

Releasing 20^101,103,105

No ecm done on the last term

I'll take 20^101 to 120 digits.

Releasing 20^101. It is now at 120 digits. The final term has been fully ECM'd.

I am now working on bringing all sequences on some bases to >= 120 digits with a fully ECM'd cofactor of >= 110 digits.

I'm starting where it is easy at the large bases and working my way down. Many large bases are already at > 120 (or 140) digits so there aren't many to work. Regardless, this will be a daunting effort so I'll have to see how far I go with it.

I've started with bases > 100000. There are 4 such bases with sequences at < 120 digits. They are:
131071, 524287, 1264460, and 2147483647.

Base 2147483647 only has 3 sequences < 120 digits. All are now complete to >= 120 digits.

I'm currently working on base 1264460. It has 9 such sequences and so will be a better test of how long this will take.

No reservation is needed. I expect each sequence to take an average of ~4 hours on a Ryzen 3950X but that could change if I get some long down-driver runs.

Jean-Luc,

When you do the next big update, you can add new base 40320 up to exponent 40 instead of 35 that I had previously suggested. I've initialized everything of both parities up to 40. No index 1's remaining.

With this, we can still have the cutoff of base 50000 for dropping the highest exponent from 40 to 35. That seemed a little better to me and I think it was your preference too.

Gary

Yes, up to exponent 50, that's my preference too.
Thank you very much Gary.
I am doing the full update, I started yesterday.

I am also analyzing the data.

The sequences of the n^n form have aroused my curiosity.
For example, only 9^9, 25^25, 49^49 seem to be Open-End !
But without much mystery, these are n numbers that are the squares of odd numbers : 3^2, 5^2, 7^2 and therefore, since the exponent can only be even, we finally have a "disguised opposite parity".
81^81 = (9^2)^(9^2) is also Open End since it is the sequence 3^(4*81) = 3^324.

On the other hand, if you perform calculations for the same parity sequences, and if you don't know which sequence to calculate, from n=84, we have only one sequence of the form n^n which ends, that is for n=86.
For the others, the calculations have not been done yet.
You may prefer them if you wish.

I also noticed that 2^2, 21^21, 70^70 end with the prime number 3.
If I put 2,21,70 in the OEIS, there is only one series that comes up : [URL]https://oeis.org/A034520[/URL] and we see that the next number is 273.
And 273^273 is way out of our range.
This is a joke of course, because I really don't see the connection between our work and A034520 in OEIS.
But I still entered 273^273 into FactorDB out of curiosity !

[QUOTE=garambois;616442]Yes, up to exponent 50, that's my preference too.
Thank you very much Gary.
I am doing the full update, I started yesterday.[/QUOTE]
I assume you mean exponent 40 for base 40320. Exponent 50 would be terrible. :-)

I'm looking forward to the big update!

Yes, exponent 40, sorry !

:smile:

Please, in OEIS, if I enter 1,2,11, there are 883 results.
But the results given show me a majority of sequences that do not start with 1,2,11, but where the 1,2,11 is right in the middle!
Does anyone know how to make OEIS give only the sequences that start with 1,2,11 without anything before?
I've already wasted almost an hour trying to figure out how to do this without success.
Thanks to you.

[QUOTE=garambois;616444]<snip>
I also noticed that 2^2, 21^21, 70^70 end with the prime number 3.
If I put 2,21,70 in the OEIS, there is only one series that comes up : [URL]https://oeis.org/A034520[/URL] and we see that the next number is 273.
And 273^273 is way out of our range.
This is a joke of course, because I really don't see the connection between our work and A034520 in OEIS.
But I still entered 273^273 into FactorDB out of curiosity ![/QUOTE]
Also out of curiosity, I put this sequence into aliqueit. I was curious if it would run a 666-digit sequence. It did and found a 19-digit factor! I entered it in the DB. I think the 643-digit cofactor looks just a little bit tough to run any more. I ECM'd it to t30 and it took longer than a normal factorization to t35. That's the slowest I've ever seen aliqueit run.

[QUOTE=garambois;616447]Please, in OEIS, if I enter 1,2,11, there are 883 results.
But the results given show me a majority of sequences that do not start with 1,2,11, but where the 1,2,11 is right in the middle!
Does anyone know how to make OEIS give only the sequences that start with 1,2,11 without anything before?
I've already wasted almost an hour trying to figure out how to do this without success.
Thanks to you.[/QUOTE]I didn't check them all (or for duplication), but I still came up with 370 sequences that start with 1, 2, 11:[code]A007931: Numbers that contain only 1's and 2's. Nonempty binary strings of length n in lexicographic order.
A054552: a(n) = 4*n^2 - 3*n + 1.
A001032: Numbers k such that sum of squares of k consecutive integers >= 1 is a square.
A217309: Minimal natural number (in decimal representation) with n prime substrings in base-9 representation (substrings with leading zeros are considered to be nonprime).
A049363: a(1) = 1; for n > 1, smallest digitally balanced number in base n.
A161708: a(n) = -n^3 + 7*n^2 - 5*n + 1.
A004642: Powers of 2 written in base 3.
A077475: Greedy powers of (8/13): Sum_{n>=1} (8/13)^a(n) = 1.
A057531: Numbers whose sum of digits and number of divisors are equal.
A077482: Number of self-avoiding walks on square lattice trapped after n steps.
A023173: Numbers k such that Fibonacci(k) == 1 (mod k).
A038725: a(n) = 6*a(n-1) - a(n-2), n >= 2, a(0)=1, a(1)=2.
A183160: a(n) = Sum_{k=0..n} C(n+k,n-k)*C(2*n-k,k).
A003579: Dowling numbers: e.g.f. exp(x + (exp(b*x) - 1)/b), with b=7.
A126916: Numbers n such that 1 + n^2 + n^4 + n^6 + n^8 + n^10 + n^12 + n^14 + n^16 + n^18 + n^20 + n^22 + n^23 is prime.
A346650: a(n) = Sum_{k=0..n} binomial(n,k) * binomial(8*k,k) / (7*k + 1).
A103200: a(1)=1, a(2)=2, a(3)=11, a(4)=19; a(n) = a(n-4) + sqrt(60*a(n-2)^2 + 60*a(n-2) + 1) for n >= 5.
A251663: E.g.f.: exp( 3*x*G(x)^2 ) / G(x), where G(x) = 1 + x*G(x)^3 is the g.f. <a href="/A001764" title="a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).">A001764</a>.
A271507: Number of self-avoiding walks of any length from NW to SW corners on an n X n grid or lattice.
A289675: Consider the Post tag system described in <a href="/A284116" title="a(n) = largest number of distinct words arising in Post's tag system {00, 1101} applied to a binary word w, over all startin...">A284116</a> (but adapted to the alphabet {1,2}) ; sequence lists the words that terminate in the empty word.
A049531: Number of digraphs with a source and a sink on n unlabeled nodes.
A188684: Partial sums of binomials binomial(3n,n)^2/(2n+1)^2.
A197189: a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.
A213975: List of subwords of <a href="/A003842" title="The infinite Fibonacci word: start with 1, repeatedly apply the morphism 1->12, 2->1, take limit; or, start with S(0)=2, S(1...">A003842</a> arranged in lexicographic order.
A215654: G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^3).
A231556: G.f. satisfies: A(x) = (1 - x*A(x))^2 * (2*A(x) - 1).
A322761: Irregular triangle read by rows in which n-th row lists all partitions of n, in graded reverse lexicographic ordering, using a compressed notation.
A052171: Number of directed multigraphs with loops on an infinite set of nodes containing a total of n arcs.
A108851: a(n) = 4*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 2.
A110679: a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 2, a(2) = 11.
A118969: a(n) = 2*binomial(5*n+1,n)/(4*n+2).
A153440: Numbers k such that k^9*(k^9+1)+1 is prime.
A168022: Noncomposite numbers in the eastern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
A257112: Arrange numbers in a clockwise spiral with initial terms a(1)=1, a(2)=2, a(4)=4, a(6)=6, a(8)=8, a(11)=3, a(15)=5, a(19)=7, a(23)=9; thereafter each number is relatively prime to all of its four (N,S,E,W) neighbors, but shares a factor with each of its (N,S,E,W) neighbors at distance 2 and also satisfies an additional condition stated in the comments.
A297836: Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 3*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)).  See Comments.
A338845: No nonprime digit is present in a(n) * a(n+1).
A083069: Main diagonal of number array <a href="/A083064" title="Square number array T(n,k)=(k(k+2)^n+1)/(k+1) read by antidiagonals.">A083064</a>.
A153705: Greatest number m such that the fractional part of e^<a href="/A153701" title="Minimal exponents m such that the fractional part of e^m obtains a minimum (when starting with m=1).">A153701</a>(n) <= 1/m.
A334240: a(n) = exp(-n) * Sum_{k>=0} (k + 1)^n * n^k / k!.
A349290: G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(x)^4)).
A353930: Smallest number whose binary expansion has n distinct run-sums.
A006122: Sum of Gaussian binomial coefficients [ n,k ] for q=8.
A031508: Smallest k>0 such that the elliptic curve y^2 = x^3 - k has rank n, if k exists.
A069800: Triangular array in which n-th row consists of numbers with digit sum n arranged in increasing numerical order.
A070778: Let M denote the 6 X 6 matrix = row by row /1,1,1,1,1,1/1,1,1,1,1,0/1,1,1,1,0,0/1,1,1,0,0,0/1,1,0,0,0,0/1,0,0,0,0,0/ and A(n) the vector (x(n),y(n),z(n),t(n),u(n),v(n)) = M^n*A where A is the vector (1,1,1,1,1,1); then a(n) = u(n).
A101248: Decimal Goedelization of contingent WFFs (well-formed formulas) from propositional calculus, in Richard C. Schroeppel's metatheory of <a href="/A101273" title="Theorems from propositional calculus, translated into decimal digits.">A101273</a>. Truth value depends on truth value of variables, but is neither always true (theorem) nor always false (antitheorem).
A121231: Number of n X n binary matrices M (that is, real matrices with entries 0 and 1) such that M^2 is also a binary matrix.
A135404: Gessel sequence: the number of paths of length 2m in the plane, starting and ending at (0,1), with unit steps in the four directions (north, east, south, west) and staying in the region y > 0, x > -y.
A143870: Number of ways of placing kings with no more than 1 mutual attack on an n X n chessboard.
A153706: Greatest number m such that the fractional part of e^<a href="/A153702" title="Numbers k such that the fractional part of e^k is less than 1/k.">A153702</a>(n) <= 1/m.
A166992: G.f.: A(x) = exp( Sum_{n>=1} <a href="/A005260" title="a(n) = Sum_{k = 0..n} binomial(n,k)^4.">A005260</a>(n)*x^n/n ) where <a href="/A005260" title="a(n) = Sum_{k = 0..n} binomial(n,k)^4.">A005260</a>(n) = Sum_{k=0..n} C(n,k)^4.
A254627: Indices of centered pentagonal numbers (<a href="/A005891" title="Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.">A005891</a>) that are also triangular numbers (<a href="/A000217" title="Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.">A000217</a>).
A342043: When a digit d is even, the next digit is < d.
A003442: Number of nonequivalent dissections of an n-gon into (n-3) polygons by nonintersecting diagonals rooted at a cell up to rotation.
A005366: Hoggatt sequence with parameter d=8.
A026933: Self-convolution of array T given by <a href="/A008288" title="Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.">A008288</a>.
A047854: a(n) = T(6,n), array T given by <a href="/A047848" title="Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...">A047848</a>.
A050929: Number of directed multigraphs with loops on 4 nodes with n arcs.
A054894: a(n+1) = 4*a(n) + 4*a(n-1) - 4*a(n-2) - a(n-3) with a(1)=1, a(2)=2, a(3)=11, a(4)=48.
A081926: Triangle read by rows in which n-th row gives n smallest numbers with digit sum n.
A088690: E.g.f.: A(x) = f(x*A(x)), where f(x) = (1+x)*exp(x).
A104185: Number of partitions of the set 1, 2, 3, ..., 6n+3 into 2n+1 sets of 3 elements each, such that each 3-element set has the same sum (there are no such partitions unless there are 6n+3 elements).
A105486: Number of partitions of {1...n} containing 4 strings of 3 consecutive integers, where each string is counted within a block and a string of more than 3 consecutive integers are counted three at a time.
A125064: Number of monocyclic skeletons with a ring size of n. See the paper by Hendrickson and Parks for details.
A132871: Row sums of triangle <a href="/A132870" title="Triangle T, read by rows, where the g.f. of row n of T^n = (n^2 + y)^n for 0 <= n <= 29, where T^n denotes the n-th power of...">A132870</a>.
A158837: Column 1 of triangle <a href="/A158835" title="Triangle, read by rows, that transforms diagonals in the array A158825 of coefficients of successive iterations of x*C(x) wh...">A158835</a>.
A161527: Numerators of cumulative sums of rational sequence <a href="/A038110" title="Numerator of frequency of integers with smallest divisor prime(n).">A038110</a>(k)/<a href="/A038111" title="Denominator of density of integers with smallest prime factor prime(n).">A038111</a>(k).
A216831: a(n) = Sum_{k=0..n} binomial(n,k)^3 * k!.
A343898: a(n) = Sum_{k=0..n} (k!)^3 * binomial(n,k).
A346925: a(n) = Sum_{d|n} mu(n/d) * binomial(3*d,d) / (2*d+1).
A007984: Number of essential graphs with n nodes (in 1-1 correspondence with Markov equivalence classes of acyclic digraphs).
A034726: Smallest integral value of m/(sum of digits of m) for any n-digit number m.
A063112: a(1) = 1; a(n+1) = a(n) + product of nonzero digits of a(n) when written in base 3. Display sequence in base 3.
A082266: In the array shown below the n-th row contains all the palindromes that use digits > 0 and have a digit sum of n. The sequence contains the array read by rows.
A099169: a(n) = (1/n) * Sum_{k=0..n-1} C(n,k) * C(n,k+1) * (n-1)^k.
A103336: Numbers whose largest primitive root (<a href="/A046146" title="Largest primitive root modulo n, or 0 if no root exists.">A046146</a>) is not prime.
A114175: Sums of squared terms in rows of triangle <a href="/A114172" title="Triangle, read by rows, where the g.f. of column n, C_n(x), equals the g.f. of row n, R_n(x), divided by (1-x)^(n+1), for n>...">A114172</a>.
A116990: Indices of triangular numbers whose sum of divisors is square.
A118347: Semi-diagonal (one row below central terms) of pendular triangle <a href="/A118345" title="Pendular triangle, read by rows, where row n is formed from row n-1 by the recurrence: if n > 2k, T(n,k) = T(n,n-k) + T(n-1,...">A118345</a> and equal to the self-convolution of the central terms (<a href="/A118346" title="Central terms of pendular triangle A118345.">A118346</a>).
A121337: Number of idempotent relations on n labeled elements.
A121419: Column 2 of triangle <a href="/A121416" title="Matrix square of triangle A121412.">A121416</a>.
A127668: Concatenated indices of primes in prime factorization of n.
A130288: Record indices of <a href="/A130280" title="a(n) = smallest integer k>1 such that n(k^2-1)+1 is a perfect square, or 0 if no such number exists.">A130280</a>: integers n>0 for which min{ m>1 | (2n+1)^2(m^2-1)+1 is a square} < oo but bigger than for all preceding n.
A133558: a(n) = a(n-1) + 9*a(n-2) for n >= 2, a(0)=1, a(1)=2.
A139475: Number of decimal digits in <a href="/A139474" title="a(n) = ((2*sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2*sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)).">A139474</a>(n).
A143135: E.g.f. satisfies: A(x) = sin(x + A(x)^2) with A(0)=0.
A143875: Number of ways of placing kings with no more than 2 mutual attacks on an n X n chessboard.
A166909: Row sums of triangle <a href="/A166905" title="Triangle, read by rows, that transforms rows into diagonals in the table A158825 of coefficients in successive iterations of...">A166905</a>.
A188648: Binomial sums a(n) = Sum_{k=0..n} (binomial(2n-k,k))^2.
A206401: E.g.f. A(x) satisfies: exp(A(x)) = x + exp(3*A(x)^2/2), with A(0) = 0.
A217391: Partial sums of the squares of the ordered Bell numbers (number of preferential arrangements) <a href="/A000670" title="Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; o...">A000670</a>.
A218340: Triangle T(n,k) of orders of degree-n irreducible polynomials over GF(23) listed in ascending order.
A241596: Partitions listed by alternately incrementing each part and appending a 1.
A292916: a(n) = n! * [x^n] exp(n*x)/(2 - exp(x)).
A294557: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + b(n-2) + n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A296288: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + n*b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
A318007: E.g.f. A(x) satisfies: A(x) = sin(x) + cos(x)*A(x)^2 with A(0)=0.
A327215: Self-convolution of <a href="/A008485" title="Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^n.">A008485</a>.
A343900: a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).
A344539: Lexicographically earliest sequence S of distinct positive terms such that the sum of the last k digits of S is odd, k being the rightmost digit of a(n).
A351997: A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only odd numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.
A352932: Where the parity of <a href="/A352931" title="a(n) = A093714(n) - n.">A352931</a> changes.
A355111: Expansion of e.g.f. 3 / (4 - 3*x - exp(3*x)).
A048867: Numbers for which reduced residue system contains fewer primes than nonprimes.
A066382: a(n) = Sum_{k=0..n} binomial(n^2,k).
A077805: Smallest prime factor of numbers containing in their decimal representation only the digits 0 and 1.
A079808: Consider triangle in which the 2n-th row contains first 2n positive integers in decreasing order and the (2n+1)-st row contains first 2n+1 positive integers in increasing order; sequence contains concatenation of numbers read upward at a 45-degree angle.
A081242: Left-to-right binary enumeration.
A082264: Triangle whose n-th row contains n smallest palindromes with a digit sum of n.
A098621: Consider the family of multigraphs enriched by the species of partitions. Sequence gives number of those multigraphs with n loops and edges.
A099693: Consider the family of multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n loops and edges.
A099697: Consider the family of multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n loops and edges.
A103255: Integers x > 0 such that x^3 + y^3 = z^2 for some y > 0, z > 0, and gcd(x,y) = 1.
A111081: Successive generations of an alternating Kolakoski rule.
A118805: G.f.: 1 = Sum_{n>=0} a(n)*x^n*Product_{k=1..n} (1-k*x)^2.
A121713: Inverse permutation to <a href="/A121711" title="Lexicographically earliest permutation of the natural numbers such that gcd(s(k-1)+1, a(k)) greater than gcd(s(k-1), a(k)+1)...">A121711</a>.
A122708: Number of connected parking functions of length n. This is the number of independent algebraic generators in degree n of the Hopf algebra of parking functions.
A127199: A monotonic doubly-fractal simple sequence. Erase the last (rightmost) digit of every integer: what is left is the sequence itself. The erased digits, one by one, form also the sequence itself.
A127303: A doubly-fractal simple sequence. Erase the first (leftmost) digit of every integer: what is left is the sequence itself. The erased digits, one by one, form also the sequence itself.
A128855: Number of partitions of binomial(2*n, n).
A145163: G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x)^2.
A154251: Expansion of (1-x+7x^2)/((1-x)(1-2x)).
A154887: Number of ways to partition n into distinct reduced fractions i/j with j<=n.
A181168: G.f.: 1 = 1/(1+x) + Sum_{n>=1} a(n)*C(2n,n-1)*x^n* Sum_{k>=0} C(2n+k,k)^2*(-x)^k.
A185627: Column 2 of triangle <a href="/A185624" title=" Triangle, read by rows, equal to the matrix square of triangle A185620.">A185624</a>.
A199397: Binary XOR of 3^k as k varies from 0 to n.
A204243: Determinant of the n-th principal submatrix of <a href="/A204242" title="Infinite symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=2^i-1 and f(i,j)=0 otherwise, read by antidiagonals.">A204242</a>.
A207571: G.f.: Sum_{n>=0} Product_{k=1..n} ((1+x)^(3*k-1) - 1).
A215623: G.f.: A(x) = (1 + x*A(x)) * (1 + x*A(x)^4).
A217308: Minimal natural number (in decimal representation) with n prime substrings in base-8 representation (substrings with leading zeros are considered to be nonprime).
A227465: E.g.f. equals the series reversion of arctan(x) / exp(x).
A236962: Column 1 of triangle <a href="/A236961" title="Triangle, read by rows, that transforms diagonals in the table of coefficients in the successive iterations of g.f. of A2369...">A236961</a>.
A238109: List of prefix-normal words over the alphabet {1,2}.
A245895: Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 312.
A254196: a(n) is the numerator of Product_{i=1..n} (1/(1-1/prime(i))) - 1.
A257283: Numbers n not divisible by 3 such that n^2 written in base 3 has no digit > 1.
A258221: Row sums of <a href="/A258220" title="T(n,k) = 1/k! * Sum_{i=0..k} (-1)^(k-i) *C(k,i) * A258219(n,i); triangle T(n,k), n>=0, 0<=k<=n, read by rows.">A258220</a>.
A278070: a(n) = hypergeometric([n, -n], [], -1).
A295099: a(n) = n! * [x^n] exp(n*x)/sqrt(1 - 2*x).
A299531: Solution a( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments.
A319743: Row sums of <a href="/A174158" title="Triangle read by rows: T(n,m) = (binomial(n - 1, m - 1)*binomial(n, m - 1)/m)^2.">A174158</a>.
A320095: Number of primitive (=aperiodic) n-ary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
A336034: The rightmost digit d of a(n) jumps over d digits to the right and is duplicated there. Lexicographically earliest sequence of distinct positive integers with this property.
A339807: Irregular triangle read by rows: T(n,k) (n>=2, k>=1) is the number of strong digraphs on n nodes with k descents.
A342996: The number of partitions of the n-th primorial.
A343929: a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k).
A346424: Number of partitions of the 2n-multiset {0,...,0,1,2,...,n}.
A346497: List of powers of 2 written in base 3 which contain no zero digits.
A354298: a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (2*k-1)!!.
A357820: Numerators of the partial alternating sums of the reciprocals of the Dedekind psi function (<a href="/A001615" title="Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p).">A001615</a>).
A041389: Denominators of continued fraction convergents to sqrt(209).
A041447: Denominators of continued fraction convergents to sqrt(239).
A042245: Denominators of continued fraction convergents to sqrt(648).
A042347: Denominators of continued fraction convergents to sqrt(700).
A042453: Denominators of continued fraction convergents to sqrt(754).
A042563: Denominators of continued fraction convergents to sqrt(810).
A056846: Number of polyominoids containing n squares: these are 2-dimensional polyominoes in a three-dimensional grid (edge-connected squares, like the floors, ceilings and walls of a building). Mirror images are distinguished.
A058154: Number of labeled monoids of order n with a fixed identity.
A060059: Row sums of triangle <a href="/A060058" title="Triangle of numbers related to A000330 (sum of squares) and A000364 (Euler numbers).">A060058</a>.
A067931: Numbers k that divide the alternating sum sigma(1) - sigma(2) + sigma(3) - sigma(4) + ... + ((-1)^(k+1))*sigma(k).
A098437: Row sums in triangle of 3rd central factorial numbers (<a href="/A098436" title="Triangle of 3rd central factorial numbers T(n,k).">A098436</a>).
A099701: Consider the family of multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n loops and edges.
A099713: Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n loops and edges.
A106371: Representation of n in base b, where b is minimal such that n contains no zeros: b = <a href="/A106370" title="Smallest b>1 such that n contains no zeros in its base b representation.">A106370</a>(n).
A111090: Successive generations of an alternating Kolakoski rule.
A111535: a(n) = <a href="/A111534" title="Main diagonal of table A111528.">A111534</a>(n)/n = <a href="/A111528" title="Square table, read by antidiagonals, where the g.f. for row n+1 is generated by: x*R_{n+1}(x) = (1+n*x - 1/R_n(x))/(n+1) wit...">A111528</a>(n,n)/n for n>=1.
A112288: Numerator of sum{k=1 to n} 1/s(n,k), where s(n,k) is an unsigned Stirling number of the first kind.
A114179: Sums of squared terms in rows of triangle <a href="/A114176" title="Triangle, read by rows, where the g.f. of column n, C_n(x), equals the g.f. of row n, R_n(x), divided by (1-x)^(n+1)*(1-x^2)...">A114176</a>.
A116437: Numbers n which when sandwiched between two 2's give a multiple of n.
A118802: Row squared sums of triangle <a href="/A118801" title="Triangle T that satisfies the matrix products: C*[T^-1]*C = T and T*[C^-1]*T = C, where C is Pascal's triangle.">A118801</a>: a(n) = Sum_{k=0..n} <a href="/A118801" title="Triangle T that satisfies the matrix products: C*[T^-1]*C = T and T*[C^-1]*T = C, where C is Pascal's triangle.">A118801</a>(n,k)^2.
A124836: Central terms of even-indexed rows in triangle <a href="/A124834" title="Triangle, read by rows, where the g.f. of column k, C_k(x), is equal to the product: C_k(x) = Product_{k=0..n} 1/(1 - binomi...">A124834</a>.
A134096: Define G(x) = Sum_{n>=0} a(n)*x^n/2^[n*(n-1) - <a href="/A000120" title="1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).">A000120</a>(n)], then [x^n] G(x)^(1/2^n) = 1 for n>=0, where <a href="/A000120" title="1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).">A000120</a>(n) = number of 1's in binary expansion of n.
A136407: Valid strings, in lexicographic order, of Balls ("1") and Strikes ("2") in a Baseball at-bat. Numbers that contain only 1's and 2's never exceeding 3 total 2's or 4 total 1's, whichever comes first.
A137904: Rows 1, 3, 5, 7 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.
A140148: a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^0 if n is even.
A140314: Number of n X n binary matrices containing no more than two 1's in any 2 X 2 sub-block.
A140322: a(n) = -1/6 + (-1)^n/2 + 2*4^n/3.
A145512: Number of partitions of 9^n into powers of 9.
A145523: Least integer k > 0 such that <a href="/A000041" title="a(n) is the number of partitions of n (the partition numbers).">A000041</a>(k) is divisible by 2^n.
A153298: G.f.: A(x) = F(x*G(x)^3)^2 = F(G(x)-1)^2 where F(x) = G(x/F(x)) = 1 + x*F(x)^2 is the g.f. of <a href="/A000108" title="Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).">A000108</a> (Catalan) and G(x) = F(x*G(x)) = 1 + x*G(x)^3 is the g.f. of <a href="/A001764" title="a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).">A001764</a>.
A153393: G.f.: A(x) = F(x*G(x)^2)^2 where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of <a href="/A001764" title="a(n) = binomial(3*n,n)/(2*n+1) (enumerates ternary trees and also noncrossing trees).">A001764</a> and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of <a href="/A000108" title="Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).">A000108</a> (Catalan).
A158098: Euler transform of triangular powers of 2: [2,2^3,2^6,...,2^(n(n+1)/2),...].
A160852: Chebyshev transform of <a href="/A107841" title="Series reversion of x(1-3x)/(1-x).">A107841</a>.
A162468: Integers n such that <a href="/A000009" title="Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd p...">A000009</a>(n) (the number of partitions of n into distinct parts) == 1 (mod n).
A164581: a(n) = 5*a(n - 1) + a(n - 2), with a(0)=1, a(1)=2.
A166989: G.f.: A(x) = 1/(1 - 2*x - 7*x^2 - 2*x^3 + x^4).
A185545: Numbers n such that there exists a sequence of n consecutive perfect squares that add up to a perfect square.
A190261: Continued fraction of (1 + sqrt(1 + 2x))/2, where x=sqrt(2).
A206846: G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2,k^2) * binomial(n^2,(n-k)^2) ).
A216585: G.f.: exp( Sum_{n>=1} <a href="/A000984" title="Central binomial coefficients: binomial(2*n,n) = (2*n)!/(n!)^2.">A000984</a>(n)*<a href="/A002426" title="Central trinomial coefficients: largest coefficient of (1 + x + x^2)^n.">A002426</a>(n)*x^n/n ), where <a href="/A000984" title="Central binomial coefficients: binomial(2*n,n) = (2*n)!/(n!)^2.">A000984</a> is the central binomial coefficients and <a href="/A002426" title="Central trinomial coefficients: largest coefficient of (1 + x + x^2)^n.">A002426</a> is the central trinomial coefficients.
A217306: Minimal natural number (in decimal representation) with n prime substrings in base-6 representation (substrings with leading zeros are considered to be nonprime).
A220771: Number of tilings of a 5 X n rectangle using integer-sided rectangular tiles of equal area.
A222080: G.f.: 1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^2.
A227466: E.g.f. equals the series reversion of tanh(x) / exp(x).
A231229: G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (2*k - x) / (1 - 2*k*x).
A235609: List of privileged words over the alphabet {1,2}.
A239741: Numbers k such that prime(k) * 2^k - 1 is prime.
A243950: Sum of the squares of q-binomial coefficients for q=2 in row n of triangle <a href="/A022166" title="Triangle of Gaussian binomial coefficients (or q-binomial coefficients) [n,k] for q = 2.">A022166</a>, for n>=0.
A245054: Number of hybrid (n+1)-ary trees with n internal nodes.
A259213: Column 2 of triangle <a href="/A258829" title="Number T(n,k) of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal va...">A258829</a>.
A274736: G.f. A(x) satisfies: A(x)^2 - 4*A(x)^3 = A(x^2).
A279202: Number of Wilf-equivalence classes of square permutations of 2n things that avoid 132.
A294547: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 2n, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A294551: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + b(n-2) + 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A296285: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + n*b(n-2), where a(0) = 1, a(1) = 2, b(0) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
A297545: Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.
A299973: Lexicographic first sequence of positive integers such that a(n) + a(n+1) has a digit 3, and no term occurs twice.
A307770: Expansion of e.g.f. 1/(1 - Sum_{k>=1} prime(k)*x^k/k!).
A324445: Number of labeled cyclic chord diagrams with n chords such that the minimal chord length equals one.
A333861: The sum of the Hamming weights of the elements of the Collatz orbit of n.
A341955: G.f. B(x) satisfies: B(x) = 1/((1-x*A(x))*(1-x*C(x)^3)) such that A(x) = 1/((1-x*B(x)^2)*(1-x*C(x)^3)) and C(x) = 1/((1-x*A(x))*(1-x*B(x)^2)) are the g.f.s of <a href="/A341954" title="G.f. A(x) satisfies: A(x) = 1/((1-x*B(x)^2)*(1-x*C(x)^3)) such that B(x) = 1/((1-x*A(x))*(1-x*C(x)^3)) and C(x) = 1/((1-x*A(...">A341954</a> and <a href="/A341956" title="G.f. C(x) satisfies: C(x) = 1/((1-x*A(x))*(1-x*B(x)^2)) such that A(x) = 1/((1-x*B(x)^2)*(1-x*C(x)^3)) and B(x) = 1/((1-x*A(...">A341956</a>, respectively.
A342357: Number of fundamentally different rainbow graceful labelings of graphs with n edges.
A343896: a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * binomial(n,k) * binomial(2*n+1,k).
A348859: G.f. A(x) satisfies: A(x) = 1 / ((1 - x) * (1 - x * A(4*x))).
A352292: Expansion of e.g.f. 1/(2 - exp(x) - x/(1 - x)).
A357845: Numerators of the partial alternating sums of the reciprocals of the sum of divisors function (<a href="/A000203" title="a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).">A000203</a>).
A018737: Divisors of 946.
A023642: Vertex-transitive graphs of valency 7 with 2n nodes.
A024721: a(n) = (1/5)*(4 + sum of C(5k,k)) for k = 0,1,2,...,n.
A027201: a(n) = self-convolution of row n of array T given by <a href="/A026714" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k)...">A026714</a>.
A027736: Number of independent subsets of nodes in graph formed from n-fold subdivision of 9-dimensional simplex.
A036076: E.g.f.: exp((exp(p*x)-p-1)/p+exp(x)) for p=6.
A036996: Number of isomers of alkyl homologs of adamantane with n carbon atoms.
A037091: Lexicographically earliest strictly increasing base 3 autovarious sequence: a(n) = number of distinct a(k) mod 3^n (written in base 3).
A048500: a(n) = 2^(n-1)*(7*n-12)+7.
A053880: Numbers k such that k^2 contains only digits {1,2,4}.
A054665: Number of 6-ary Lyndon words with trace 0 mod 6.
A057213: Second term of continued fraction for exp(n).
A061677: When squared gives number composed just of the digits 1, 2, 3, 4.
A063587: Smallest k such that 5^k has exactly n 2's in its decimal representation.
A076206: Numbers with digital root equal to their number of divisors.
A079009: Least k such that the 2^n successive values of phi(k+j) (j=0..2^n-1) are all distinct.
A086406: Main diagonal of number array <a href="/A086404" title="Square array of numbers T(n,k) = ((1+sqrt(3))*(k+sqrt(3))^n-(1-sqrt(3))*(k-sqrt(3))^n)/(2*sqrt(3)), read by antidiagonals.">A086404</a>.
A094955: Main diagonal of array <a href="/A094954" title="Array T(k,n) read by antidiagonals. G.f.: x(1-x)/(1-kx+x^2), k>1.">A094954</a>.
A102343: Numbers k such that k*10^3 + 777 is prime.
A109858: The n-th row of the following array contains all palindromes, with at most n digits, with digit sum n. Sequence contains the array by rows.
A110329: Diagonal sums of a number triangle related to the Pell numbers.
A116038: n+p(n)+p(p(n)) is a brilliant number (<a href="/A078972" title="Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits.">A078972</a>), where p(n) denotes the n-th prime.
A119438: Number of sets of points determined by the intersection of a line with an n X n grid of points.
A120380: Number of partitions of n*(n+1).
A120445: Number of different convex inscribed polygons with n pair of sides of lengths d1, d2, ..., dn all distinct. Or number of bracelets with n pairs of beads, each pair of one among n colors.
A130222: Number of partitions of 2n-set in which number of blocks of size 2k-1 is even (or zero) for every k.
A136317: a(n) integers with digit sum a(n); a(n+1) is the smallest integer > a(n).
A136970: Numbers k such that k and k^2 use only the digits 1, 2, 3, 4 and 7.
A136971: Numbers k such that k and k^2 use only the digits 1, 2, 3, 4 and 8.
A136997: Numbers k such that k and k^2 use only the digits 1, 2, 4, 7 and 8.
A141314: Euler transform of <a href="/A141313" title="Number of connected 2-colored parking functions.">A141313</a>.
A155928: G.f. satisfies: A(x) = F(x)^2 where F(x) = Sum_{n>=0} <a href="/A155926" title="G.f. satisfies: A(x) = B(x*A(x)) where A(x) = Sum_{n>=0} a(n)*x^n/[n!*(n+1)!/2^n] and B(x) = Sum_{n>=0} x^n/[n!*(n+1)!/2^n].">A155926</a>(n)*x^n/[n!*(n+1)!/2^n] and A(x) = Sum_{n>=0} a(n)*x^n/[n!*(n+1)!/2^n].
A173638: The n-th semiprime plus n gives a palindrome in base 10.
A179462: Least natural number n in increasing order such that the sum of decimal digits is equal to <a href="/A001223" title="Prime gaps: differences between consecutive primes.">A001223</a>(n).
A181270: Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly increasing order.
A181369: Number of maximal rectangles in all L-convex polyominoes of semiperimeter n. An L-convex polyomino is a convex polyomino where any two cells can be connected by a path internal to the polyomino and which has at most 1 change of direction (i.e., one of the four orientations of the letter L). A maximal rectangle in an L-convex polyomino P is a rectangle included in P that is maximal with respect to inclusion.
A188203: G.f.: exp( Sum_{n>=1} <a href="/A188202" title="Central coefficients in (1 + 2^n*x + x^2)^n.">A188202</a>(n)*x^n/n ) where <a href="/A188202" title="Central coefficients in (1 + 2^n*x + x^2)^n.">A188202</a>(n) = [x^n] (1 + 2^n*x + x^2)^n.
A197642: Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,2,0,2 for x=0,1,2,3,4.
A198894: a(n) = <a href="/A198893" title="Number of strictly increasing Boolean functions of n variables.">A198893</a>(n)/n!.
A202140: Size of the largest semigroup generated by two n X n Boolean matrices.
A203534: G.f.: exp( Sum_{n>=1} sigma(n)*<a href="/A002203" title="Companion Pell numbers: a(n) = 2*a(n-1) + a(n-2), a(0) = a(1) = 2.">A002203</a>(n)*x^n/n ) where <a href="/A002203" title="Companion Pell numbers: a(n) = 2*a(n-1) + a(n-2), a(0) = a(1) = 2.">A002203</a> is the companion Pell numbers.
A205073: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 6,6,2,0,0,0,1 for x=0,1,2,3,4,5,6
A209604: Number of nX2 1..2 arrays with every element value z a city block distance of exactly z from another element value z
A214215: List of subwords (or factors) of the Thue-Morse "1,2"-word <a href="/A001285" title="Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtain...">A001285</a>.
A216213: Numbers k such that sigma*(k) = Sum_{j=anti-divisors of k} sigma*(j), where sigma*(k) is the sum of the anti-divisors of k.
A233445: Start of record runs with lambda(k) = lambda(k+1) = ..., where lambda is Liouville's function <a href="/A008836" title="Liouville's function lambda(n) = (-1)^k, where k is number of primes dividing n (counted with multiplicity).">A008836</a>.
A248118: Number of subsets of {1,...,n} containing n and having at least one set partition into 9 blocks with equal element sum.
A250887: G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 3*A(x)).
A253256: G.f. satisfies: A(x) = (1 - x^3*A(x)^6) / (1 - x*A(x)^2)^2.
A262547: Nearest integer to 2^(2^n)/(4*n!).
A263720: Palindromic numbers such that the sum of the digits equals the number of divisors.
A275536: Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.
A288945: Starting with a(1) = 1, a(n) = smallest nonnegative integer not yet in the sequence such that the first digit of a(n) is the last digit of a(n-1) plus or minus 1, with preference given to -1 when possible. The digit 0 is not allowed.
A292424: a(n) = [x^n] Product_{k=1..n} 1/((1 - x)^k * (1 - x^k)).
A293240: Number of matchings in the n-Mycielski graph.
A293574: a(n) = Sum_{k=0..n} n^(n-k)*binomial(n+k-1,k).
A309068: Least k such that the rank of the elliptic curve y^2 = x^3 - k^2 is n.
A342945: Numbers m such that d(1)^1 + d(2)^2 + ... + d(p)^k = d(1)! + d(2)! + ... + d(k)!, where d(i), i=1..k, are the digits of m.
A349023: G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4)^2.
A349639: a(n) = Sum_{k=0..n} binomial(n,k) * <a href="/A000108" title="Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).">A000108</a>(k) * k^k.
A354978: a(n) = Sum_{k=0..n} Stirling2(k + n, n), row sums of <a href="/A354977" title="Triangle read by rows. T(n, k) = Sum_{j=0..n}((-1)^(n-j)*binomial(n, j)*j^(n+k)) / n!.">A354977</a>.
A355425: Expansion of e.g.f. 1/(1 - Sum_{k=1..2} (exp(k*x) - 1)/k).
A356523: a(n) is the number of tilings of the Aztec diamond of order n using dominoes and horizontal straight tetrominoes.
A356567: Numbers that generate increasing numbers of consecutive primes when doubled and added to the sequence of odd squares. (Positions of records in <a href="/A354499" title="Number of consecutive primes generated by adding 2n to the odd squares (A016754).">A354499</a>.)
A011839: f-vectors for 7-neighborly simplicial complexes on n+6 vertices.
A018351: Divisors of 242.
A018375: Divisors of 286.
A018420: Divisors of 374.
A018443: Divisors of 418.
A018491: Divisors of 506.
A018563: Divisors of 638.
A018590: Divisors of 682.
A018661: Divisors of 814.
A018711: Divisors of 902.
A020559: Number of ordered multigraphs on n labeled edges (with loops).
A026946: Self-convolution of array T given by <a href="/A026374" title="Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0, T(n,k) = T(n-1,k-1) + T(n-1,k) for odd n and 1< = k <= ...">A026374</a>.
A026956: a(n) = self-convolution of array T given by <a href="/A026615" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(n,1)=T(n,n-1)=2n-1 for n >= 1; T(n,k)=T(n-1,k-1)+T(n-1,k) for...">A026615</a>.
A026961: a(n) = self-convolution of array T given by <a href="/A026626" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(n,1)=T(n,n-1)=[ 3n/2 ] for n >= 1; T(n,k)=T(n-1,k-1)+T(n-1,k)...">A026626</a>.
A026971: a(n) = self-convolution of array T given by <a href="/A026648" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k)...">A026648</a>.
A026981: a(n) = self-convolution of array T given by <a href="/A026670" title="Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 1, T(n,1) = T(n,n-1) = n+1; for n >= 2, T(n,k) = T...">A026670</a>.
A026986: Self-convolution of array T given by <a href="/A026681" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-1,k) if k or n-...">A026681</a>.
A026996: Self-convolution of array T given by <a href="/A026703" title="Triangular array T read by rows: T(n,1) = T(n,n) = 1, T(n,k) = T(n-1, k-1) + T(n-2,k-1) + T(n-1,k) if k=(n/2) or k=((n+1)/2)...">A026703</a>.
A027223: a(n) = self-convolution of row n of array T given by <a href="/A026747" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) ...">A026747</a>.
A027229: a(n) = sum of squares of numbers in row n of array T given by <a href="/A026747" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) ...">A026747</a>.
A027247: a(n) = self-convolution of row n of array T given by <a href="/A026780" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) ...">A026780</a>.
A027253: Sum of squares of numbers in row n of array T given by <a href="/A026780" title="Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) ...">A026780</a>.
A034039: Numbers that are primitively but not imprimitively represented by (x^2+xy+2y^2, x>=0, y>=0).
A037089: Lexicographically earliest strictly increasing decimal autovarious sequence: a(n) = number of distinct n-digit endings (left-zero-padded) of elements in the sequence.
A038113: Lexicographically earliest strictly increasing base 4 autovarious sequence: a(n) = number of distinct a(k) mod 4^n (written in base 4).
A038114: Lexicographically earliest strictly increasing base 5 autovarious sequence: a(n) = number of distinct a(k) mod 5^n (written in base 5).
A038115: Lexicographically earliest strictly increasing base 6 autovarious sequence: a(n) = number of distinct a(k) mod 6^n (written in base 6).
A038116: Lexicographically earliest strictly increasing base 7 autovarious sequence: a(n) = number of distinct a(k) mod 7^n (written in base 7).
A038117: Lexicographically earliest strictly increasing base 8 autovarious sequence: a(n) = number of distinct a(k) mod 8^n (written in base 8).
A038118: Lexicographically earliest strictly increasing base 9 autovarious sequence: a(n) = number of distinct a(k) mod 9^n (written in base 9).
A038217: Triangle whose (i,j)-th entry is binomial(i,j)*2^(i-j)*11^j.
A043080: a(n)=(s(n)+9)/10, where s(n)=n-th base 10 palindrome that starts with 1.
A087552: a(1) = 1, then the smallest prime divisor of <a href="/A065447" title="Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).">A065447</a>(n) not included earlier.
A090323: Literal string created by the first time an orderless exponent appears; the exponents from <a href="/A025487" title="Least integer of each prime signature A124832; also products of primorial numbers A002110.">A025487</a>.
A096109: Beginning with 1 distinct numbers. A new digit say n occurs after exhausting all possible numbers containing up to and at most n-1 digits, in increasing order (in a typical manner explained in the example) formed by already occurring digits.
A099933: Main diagonal of array <a href="/A007754" title="Array (a frieze pattern) defined by a(n,k) = (a(n-1,k)*a(n-1,k+1) - 1) / a(n-2,k+1), read by antidiagonals.">A007754</a>.
A100109: a(n) = n^3 - 2*n^2 + 2.
A104085: Coefficient list length of Poincaré-like polynomials made from <a href="/A047845" title="(n-1)/2, where n runs through odd nonprimes (A014076).">A047845</a>, indices of odd nonprimes (group dimension equivalent plus one).
A109868: Numbers which can be differences of successive palindromes in order of their first occurrence.
A113626: Numbers simultaneously heptagon-free, pentagon-free, squarefree and triangle-free.
A114034: Let f(n) be the number of sequences of 1's and 2's which sum to n. Sequence contains the string of sequences.
A115095: Positions of 4 in <a href="/A038800" title="Number of primes between 10n and 10n+9.">A038800</a>.
A116586: The symbol numbers of the IChing in rectangular/ square array taken as an antidiagonal.
A136967: Numbers k such that k and k^2 use only the digits 1, 2, 3 and 4.
A136986: Numbers k such that k and k^2 use only the digits 1, 2 and 4.
A136996: Numbers k such that k and k^2 use only the digits 1, 2, 4 and 7.
A136999: Numbers k such that k and k^2 use only the digits 1, 2, 4 and 8.
A137001: Numbers k such that k and k^2 use only the digits 1, 2, 4 and 9.
A138552: Returning walks of length 2n on the upper half of the square lattice, distinct under reflections about the y-axis.
A140305: Number of n X n binary matrices containing no more than two 1s in any 3 X 3 sub-block.
A151314: Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, -1), (0, 1), (1, -1), (1, 1)}.
A151418: Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 1), (1, -1), (1, 0), (1, 1)}
A153304: G.f. satisfies: A(x) = x + 2*A(x)^2 + 3*A(x)*A(A(x))^2 + 4*A(x)*A(A(x))*A(A(A(x)))^2 +...
A158265: G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n+1)*x^n/n ).
A168498: The positions of non-single or nonisolated numbers in <a href="/A000010" title="Euler totient function phi(n): count numbers <= n and prime to n.">A000010</a>.
A175927: Duplicate of <a href="/A116990" title="Indices of triangular numbers whose sum of divisors is square.">A116990</a>.
A197336: Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,3,2,1,2 for x=0,1,2,3,4
A197718: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 4,4,2,0,1,0,0 for x=0,1,2,3,4,5,6
A197794: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 5,4,2,0,1,1,0 for x=0,1,2,3,4,5,6
A197900: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 6,4,2,0,1,1,1 for x=0,1,2,3,4,5,6
A197914: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 5,4,2,0,1,2,0 for x=0,1,2,3,4,5,6
A197993: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 6,5,2,0,0,0,2 for x=0,1,2,3,4,5,6
A197994: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 6,4,2,0,1,0,2 for x=0,1,2,3,4,5,6
A198001: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 5,5,2,0,0,2,0 for x=0,1,2,3,4,5,6
A198088: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 4,4,2,0,1,2,0 for x=0,1,2,3,4,5,6
A203203: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 6,4,2,0,0,0,2 for x=0,1,2,3,4,5,6
A205806: E.g.f. A(x) satisfies: A( cos(x) - exp(-x) ) = x.
A207155: Number of nXnXn 0..6 triangular arrays with each element x equal to the number its neighbors equal to 5,5,2,0,0,1,0 for x=0,1,2,3,4,5,6
A220095: n such that there are no primes between n - sqrt(n) and n.
A220878: Number of Catalan M-paths.
A250221: Least k such that A_n(k) = n, or -1 if no such k exists.
A256933: Numbers k such that R_(k+2) + 7*10^k is prime, where R_k = 11...1 is the repunit (<a href="/A002275" title="Repunits: (10^n - 1)/9. Often denoted by R_n.">A002275</a>) of length k.
A268294: E.g.f. satisfies: A(x) = Sum_{n>=1} [Integral exp(n*A(x)) dx]^n/n.
A279703: Number of n X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
A285199: Product of n! and the n-th Legendre polynomial evaluated at 2.
A287395: Indices of records in <a href="/A286720" title="Number of Egyptian fractions in the representation of 1-1/(2n+1) by the odd greedy expansion algorithm, without repeats.">A286720</a>.
A290873: Number of minimal dominating sets in the n-transposition graph.
A291263: Number of maximal irredundant sets in the n-transposition graph.
A296053: Numbers k such that (46*10^k + 683)/9 is prime.
A305537: G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x*A(x)/(1 - x*A(x) - 2*x*A(x)/(1 - x*A(x) - 3*x*A(x)/(1 - x*A(x) - 4*x*A(x)/(1 - ...))))), a continued fraction.
A337012: a(n) = exp(-1/2) * Sum_{k>=0} (2*k + n)^n / (2^k * k!).
A337017: a(n) is the dimension of the Lie-admissible operad of degree n.
A343450: Integers whose nonincreasing digits are at most one more than their position.
A346144: Number of maximal irredundant sets in the n-Bruhat graph.
A088306: Integers n with tan n > |n|, ordered by |n|.
A350932: Minimal determinant of an n X n Toeplitz matrix using the first 2*n - 1 prime numbers.
A292779: Interpret the values of the Moebius function mu(k) for k = n to 1 as a balanced ternary number.
A345035: a(n) = Sum_{k=1..n} (-3)^(floor(n/k) - 1).
A285866: a(n) = numerator((-2)^n*Sum_{k=0..n} binomial(n,k) * Bernoulli(k, 1/2)).
A015180: Sum of (Gaussian) q-binomial coefficients for q=-14.[/code]I used the following BASH script:[code]#!/bin/bash

rm tempresults 2>/dev/null
for i in {0..880..10}
do
wget "https://oeis.org/search?q=1%2c2%2c11&start=${i}" -q -O tempOEIS.html

exec <"tempOEIS.html"
while read line
do
case $line in
*"<tt><b style"*) #echo "$line"
read line
read line
echo -n "${line:25:7}: " >>tempresults
echo "$templine" >>tempresults
;;
*"<td valign=top align=left>"*) read templine
;;
esac
done
done[/code]

Wow, I didn't think there would be so many !
Thank you very much Edwin for this solution.
And do you know of any instruction or syntax that can be used directly on the OEIS to filter sequences in this way ?

Complete update of the page done.
Thanks to all for your help.

[B]Added bases : 40320, 1547860.
Removed LaurV reservations for base 28 and SuikaPredator for base 20.
[/B]
For your information : I will be away from home from tomorrow Tuesday until Saturday and I will not have any access to my computers.
But I will answer all messages when I get back.

Karsten's scripts give the sequences below as being at index 1 :
[CODE] 102 85 172 165
102 86 174 162
102 92 186 183
104 94 190 155
104 95 192 162
105 86 174 174
105 90 182 156
105 94 191 162
119 80 166 157
119 88 183 166
119 94 195 181
120 80 167 163
120 83 174 163
120 85 178 158
120 90 188 166
120 91 190 153
120 95 198 182
1352 52 163 154
14264 40 167 159
1547860 29 180 135
162 85 189 183
162 86 191 156
162 87 193 166
162 89 197 167
162 90 200 184
173 83 184 162
18 135 170 164
193 83 188 176
200 73 169 159
200 77 178 154
210 73 171 150
210 78 182 179
220 75 176 166
220 80 188 170
229 79 185 181
231 67 159 150
231 69 164 160
231 76 180 164
26 116 165 157
276 69 169 157
28 113 164 157
28 114 166 150
28 116 168 152
284 69 170 150
31704 38 172 171
31704 39 176 153
34 104 160 154
34 107 164 161
35 98 151 150
39 99 158 152
39 106 169 160
392 64 167 159
392 65 169 166
396 62 162 155
40 106 170 150
40 107 172 152
52 91 157 151
54 99 172 163
55 94 164 150
56 91 160 153
56 97 170 150
56 98 172 154
57 95 167 161
57 100 176 154
60 96 172 163
60 100 179 151
62 89 160 154
62 92 165 151
62 96 173 158
63 97 175 150
6469693230 16 158 156
6469693230 18 178 166
65 89 161 155
65 98 178 153
68 92 169 161
68 97 178 170
68 99 182 157
68 100 184 170
69 91 168 151
69 97 179 177
696 60 171 152
70 89 165 162
72 98 183 178
74 90 169 151
74 97 182 169
74 98 184 178
75 86 162 154
75 92 173 156
75 96 180 153
76 85 160 154
76 95 179 173
77 89 168 163
77 90 170 156
77 97 183 175
78 89 169 161
78 91 173 167
78 94 179 171
78 97 184 170
78 98 186 184
78 99 188 176
780 58 169 162
80 88 168 151
80 92 176 159
80 95 181 152
82 93 179 151
84 89 172 162
84 94 182 178
84 100 193 158
85 82 158 154
8589869056 19 189 162
8589869056 20 199 168
86 80 155 150
86 95 184 178
86 96 186 166
86 98 190 160
86 99 192 189
87 83 161 153
87 94 183 160
87 96 186 176
87 100 194 173
88 95 185 167
88 96 187 158
882 55 163 156
882 59 175 168
888 59 175 159
888 60 178 165
90 95 187 163
91 91 178 169
91 93 182 153
91 95 186 165
91 96 188 163
91 97 190 175
92 95 187 170
92 97 191 182
92 99 195 151
93 93 183 162
93 99 195 154
94 83 164 157
94 84 166 150
94 91 180 172
94 92 182 170
94 96 190 167
94 97 192 164
94 99 196 164
94 100 198 156
95 78 154 151
95 90 178 153
95 94 186 186
95 96 190 175
95 99 196 180
96 81 161 153
96 84 167 155
96 86 171 166
96 94 187 181
96 97 193 180
96 98 195 170
96 99 197 179
966 54 162 153
98 98 196 179
99 82 164 153
99 86 172 170
99 98 196 178
99 99 198 181
996 59 178 164 [/CODE]

One index 1 from a new base and all else matches between our index 1 lists.

Thanks for all the work keeping the tables straight.

As for the OEIS, here's a more generic script you can try. Simply use a space delimited set of elements, like [C]1 2 11 125[/C] inside the quotes for the sequence variable and it should give only the sequences that start with that set, instead of anywhere within:[code]#!/bin/bash
##################################################
## This script is designed to harvest sequences ##
## from OEIS and place the results in the file ##
## tempresults. Enter the sequence elements ##
## into the sequence variable below with spaces ##
## separating the elements and run with: ##
## bash <filename> (ex. bash oeis.sh) ##
##################################################

sequence="1 2 11 125"

seq=($sequence)
seq2=${seq[0]}
temp=1
while [ $temp -lt ${#seq[@]} ]
do
seq2="${seq2}%2c${seq[$temp]}"
let temp=${temp}+1
done

rm tempresults 2>/dev/null
page=0
lastpage=1
while [ $page -lt $lastpage ]
do
wget "https://oeis.org/search?q=${seq2}&start=${page}" -q -O tempOEIS.html

exec <"tempOEIS.html"
while read line
do
case $line in
*"<tt><b style"*) #echo "$line"
read line
read line
echo -n "${line:25:7}: " >>tempresults
echo "$templine" >>tempresults
;;
*"<td valign=top align=left>"*) read templine
;;
*"&start="*) lastpage=${line}
;;
esac
done
amp=$(echo `expr index "$lastpage" \&`)
lastpage=${lastpage:${amp}+6}
amp=$(echo `expr index "$lastpage" \&`)
if [ $amp -gt 0 ]
then
lastpage=0
else
gt=$(echo `expr index "$lastpage" \>`)
lastpage=${lastpage:0:${gt}-2}
fi
let page=${page}+10
done[/code]The results will be in the file tempresults.

[QUOTE=EdH;616481]One index 1 from a new base and all else matches between our index 1 lists.
<snip>[/QUOTE]

And that one index 1 from new base 1547860 is no longer. :-)

[QUOTE=gd_barnes;616483]And that one index 1 from new base 1547860 is no longer. :-)[/QUOTE]And, after I added it to my master list? Which is, of course, no problem, since the list is taken care of each time I run the script.:smile: In fact, unlike the other thread, the index 1 thread script is entirely complete from start to post text, when run. The other needs a small amount of interaction dealing with reservations and crediting.

[QUOTE=EdH;616481]
As for the OEIS, here's a more generic script you can try. Simply use a space delimited set of elements, like [C]1 2 11 125[/C] inside the quotes for the sequence variable and it should give only the sequences that start with that set, instead of anywhere within:
...
...
The results will be in the file tempresults.[/QUOTE]

Thank you so much Edwin, I will study this when I get back !