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2020-08-26, 08:20   #507
garambois

Oct 2011

22×5×19 Posts

Quote:
 Originally Posted by yoyo I take base 12. Do I take too much? On base 13 are some reservations.

OK, thanks a lot !
At the next update, I will reserve the base 12 for you.
No, you don't take too much !
It all depends on YAFU's computing means.
YAFU's statistics are very high at the moment.
I don't know if a team is raiding on YAFU and if the statistics will stay so high in the next few times ?

2020-08-26, 08:48   #508
garambois

Oct 2011

22·5·19 Posts

Quote:
 Originally Posted by EdH OK! I think I have them all sorted correctly, now. Attached is a new document with bases AND powers sorted (and, the power expansion is to the end).

Ok, this time the file is perfect !
Thanks a lot Ed.

I examined it closely.
Unfortunately, nothing special catches my attention at the moment.
Except a detail for the prime number 53 : there are only sequences that start on powers of 2 that end with the prime number 53. But this must be pure chance !

But maybe someone else will observe something interesting...

 2020-08-26, 09:46 #509 garambois     Oct 2011 1011111002 Posts I would also like to make a comment about a private conversation that Edwin Hall and I had in early July. Edwin allowed me to talk about this private conversation here when the messages are readable by everyone. Here is Edwin's observation : Code: Sequences that had abundant indices somewhere and a parity change other than at index 1 (all were due to perfect squares): (2^9, 2^62, 2^210): 81 >> 40 (2^12, 2^141, 2^278, 2^387): 49 >> 8 (2^112): 2209 >> 48 (2^117): 25921 >> 5600 (2^141): (729 >> 364) and (49 >> 8) (2^243): 1225 >> 542 (2^271): 2025 >> 1726 (2^305, 2^317): 9 >> 4 (2^421): 169 >> 14 Of the even numbers that were due to parity flips, only 40, 48, 364 and 5600, are abundant. This means, for example, that sequences that begin with 2^9, 2^62 and 2^210 arrive on the integer 81, which is a perfect square and therefore, at the next iteration, we will have an even term (here, 40, because s(81)=40). The goal was to find parts of sequences that begin with powers of 2 and that are increasing. The terms are then abundant. I think we can generalize this study by looking at the table called "base_2_mat" that I attached to post #447. Here is an excerpt from this table : Code: prime 2 in sequence 2^1 at index 0 prime 2 in sequence 2^2 at index 0 prime 2 in sequence 2^3 at index 0 prime 2 in sequence 2^4 at index 0 3 ... prime 2 in sequence 2^9 at index 0 3 4 prime 2 in sequence 2^10 at index 0 5 ... prime 2 in sequence 2^12 at index 0 8 ... prime 2 in sequence 2^14 at index 0 7 8 prime 2 in sequence 2^15 at index 0 7 8 ... prime 2 in sequence 2^55 at index 0 14 ... prime 2 in sequence 2^59 at index 0 12 13 ... prime 2 in sequence 2^62 at index 0 26 27 ... prime 2 in sequence 2^112 at index 0 62 63 64 ... prime 2 in sequence 2^117 at index 0 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 ... prime 2 in sequence 2^141 at index 0 25 26 27 28 34 ... prime 2 in sequence 2^164 at index 0 42 ... prime 2 in sequence 2^210 at index 0 44 45 46 49 50 ... prime 2 in sequence 2^243 at index 0 128 129 130 131 ... prime 2 in sequence 2^271 at index 0 79 80 81 82 83 84 85 86 87 88 89 ... prime 2 in sequence 2^278 at index 0 51 ... prime 2 in sequence 2^305 at index 0 76 ... prime 2 in sequence 2^317 at index 0 70 ... prime 2 in sequence 2^373 at index 0 94 95 96 97 ... prime 2 in sequence 2^387 at index 0 102 ... prime 2 in sequence 2^421 at index 0 65 66 67 ... prime 2 in sequence 2^510 at index 0 125 126 ... For more readability, I removed all the lines where there was only the index 0 of concerned. There are dotted lines instead. When you see this table, you can immediately see in which sequences from base 2, the prime number 2 appears in the factorization of terms at an index other than 0. All sequences with increasing parts identified by Edwin are found in this way, plus others: those with even terms but which are in "downdriver". Unfortunately, here again: I don't notice anything about the exponents, nor the indexes that could allow to predict for which base 2 exponents, we have parts of sequences with the prime number 2 elsewhere than at the index 0 !!!
 2020-08-26, 13:05 #510 RichD     Sep 2008 Kansas 22×811 Posts I'll start work on Table n=29.
 2020-08-26, 13:37 #511 RichD     Sep 2008 Kansas CAC16 Posts Tabe n=29 This may be of interest because it flips parity. http://factordb.com/sequences.php?se...ge&fr=32&to=42
 2020-08-26, 13:37 #512 Sergiosi   Jun 2013 2·3·13 Posts Reserving 2310^25
 2020-08-26, 15:47 #513 garambois     Oct 2011 1011111002 Posts @RichD : OK for base 29. OK for 265^2, thank you very much ! This number was already in my tables... @Sergiosi : I think you have already finished the calculations for 2310^25. And moreover, it is a non-trivial end, which is rare ! Thanks a lot !
 2020-08-27, 20:40 #514 RichD     Sep 2008 Kansas 1100101011002 Posts Who has the way back merge detection meter? I believe 20^37 has merged.
2020-08-27, 21:27   #515
EdH

"Ed Hall"
Dec 2009

1101110110102 Posts

Quote:
 Originally Posted by RichD Who has the way back merge detection meter? I believe 20^37 has merged.
20^37:i1855 merges with 660:i25

2020-08-27, 22:37   #516
richs

"Rich"
Aug 2002
Benicia, California

100101010002 Posts

Quote:
 Originally Posted by richs Reserving 439^30 at i80.
439^30 is now at i124 (added 44 iterations) and a C121 level with a 2^6 * 3 guide, so I will drop this reservation. The remaining C119 term is well ecm'ed and is ready for nfs.

Taking 439^36 at i68.

 2020-08-28, 01:14 #517 RichD     Sep 2008 Kansas 22·811 Posts 19^14 might have also merged.

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