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2021-03-01, 13:28   #903
EdH

"Ed Hall"
Dec 2009

23×461 Posts

Quote:
 Originally Posted by yoyo No problem, you can factor it.
Thanks! I'll do it this morning.

2021-03-01, 13:46   #904
EdH

"Ed Hall"
Dec 2009

23·461 Posts

Quote:
 Originally Posted by garambois . . . And above all, you are missing the odd bases (with odd exponents of course) that do not appear in your table !. . .
Not sure if I'm reading this correctly, but my program ran all the matched parity sequences, both odd and even. 15^35 and the five sequences in 1155 were the only odd bases/sequences that showed up. If there are some I missed, let me know so I can try to find out why.

BTW, 6^188 is at index 2.

2021-03-01, 15:50   #905
garambois

"Garambois Jean-Luc"
Oct 2011
France

3·5·37 Posts

Quote:
 Originally Posted by EdH Not sure if I'm reading this correctly, but my program ran all the matched parity sequences, both odd and even. 15^35 and the five sequences in 1155 were the only odd bases/sequences that showed up. If there are some I missed, let me know so I can try to find out why. BTW, 6^188 is at index 2.

Unfortunately, I only saw 15^35 and the 5 sequences of the base 1155 in your results after writing post #901.
And precisely : everything is there.
15 = 3 * 5 and 1155 = 3 * 5 * 7 * 11
These are primorials without the factor 2. And there is growth from index 1 only for these two odd bases of our project and no other odd base.
This is why for a week now, I have been calculating the sequences with odd exponents for the bases 105 = 3 * 5 * 7 and 15015 = 3 * 5 * 7 * 11 * 13.
Indeed, I immediately noticed that 105^11, 105^23, 15015^11 and 15015^23 produced the same phenomenon, just like 1155^11 and 1155^23.
And I also asked on this forum on the post #870 that the bases 45, 75 and 231 be calculated, to have odd numbers of a different type than all those which already appeared in our base, to see if the phenomenon was also going to happen with them or not.

But tomorrow I'll write it all clean !

Edit : Thanks for 6^188 !

Last fiddled with by garambois on 2021-03-01 at 15:52 Reason: Thanks for 6^188

 2021-03-01, 16:17 #906 EdH     "Ed Hall" Dec 2009 Adirondack Mtns 23·461 Posts I had not included 45, 75 or 231 in my run. Only 231^17 is found by my program, but I don't know how many of the rest are not yet at index 2. I look forward to tomorrow, although I will be tied up most of the day and may not be free enough to study what you provide until Wednesday.
2021-03-01, 16:36   #907
garambois

"Garambois Jean-Luc"
Oct 2011
France

10538 Posts

Quote:
 Originally Posted by garambois Personally, it is version N ° 6 that I prefer.

Following the public dialogue between Happy5214 and I about the presentation of the page, Karsten Bonath and I then discussed the page at length.
The page did not stop evolving for several days.
Karsten had several ideas, I had several requests, and we also included the idea of ​​Happy5214's table modified for convenience.

The approach was as follows :
We have for principle that in order to be able to observe phenomena in our project, in order to be able to notice and state conjectures, we must be able to visualize the data in all possible ways.
We wanted this page to permit to do a lot of things : classify in different ways, sort, view by categories, see statistics, see sequence counters ...

And so, we want to present you with a test page.
It is under construction, but you can already make comments (positive or negative), suggestions, ask questions ...

To access this experimental page : go to the usual page (here) and click on the "Experimental version of the page" link.

2021-03-01, 17:15   #908
garambois

"Garambois Jean-Luc"
Oct 2011
France

3·5·37 Posts

Quote:
 Originally Posted by EdH I had not included 45, 75 or 231 in my run. Only 231^17 is found by my program, but I don't know how many of the rest are not yet at index 2. I look forward to tomorrow, although I will be tied up most of the day and may not be free enough to study what you provide until Wednesday.

So I had a good intuition when I asked that the base 231 be calculated !
This proves that it is not only the primorials without the factor 2 which can have this phenomenon.
But I suspect that all odd bases will have this phenomenon if we take large enough exponents !

I hope you won't be disappointed tomorrow, because in the last 24 hours you have already seen most of my work over the past three weeks.
I think my post tomorrow will be more of a summary of work that will ask questions.
Also, it will be up to each of you to look at the data to try to find something in it.
But also maybe tomorrow, when I look at all of the new data, I'll see some other stuff.
Because this work has given a different direction to the calculations for the last 15 days.
Calculations were made to see things like this and confirm or deny things that I had noticed.
Also, don't forget Edwin that this idea came to me months later when I looked again at a painting you posted last summer !
But anyway, it's going to be very difficult to make further progress in this area.
We should calculate a lot more bases, and a lot more difficult, we should complete the green columns of all the bases.
No one has the computing power to do this in a reasonable amount of time.

2021-03-01, 17:34   #909
kar_bon

Mar 2006
Germany

43×67 Posts

Quote:
 Originally Posted by garambois To access this experimental page : go to the usual page (here) and click on the "Experimental version of the page" link.
Small additional notes: Every base will be shown on it's own page but for now only base 2 is available. Also the statistic data are only filled in numbers, no real countings.

2021-03-01, 19:42   #910
EdH

"Ed Hall"
Dec 2009

71508 Posts

Quote:
 Originally Posted by garambois . . . I hope you won't be disappointed tomorrow, because in the last 24 hours you have already seen most of my work over the past three weeks. I think my post tomorrow will be more of a summary of work that will ask questions. . . .
I don't think you'll disappoint. There will be inspiration to find ways to harvest new data. And, I agree with something else you said recently. It is great when we find the same results using entirely different methods.

 2021-03-01, 23:48 #911 RichD     Sep 2008 Kansas 63638 Posts Initializing base 38.
2021-03-02, 04:23   #912
Happy5214

"Alexander"
Nov 2008
The Alamo City

2·7·41 Posts

Quote:
 Originally Posted by garambois Following the public dialogue between Happy5214 and I about the presentation of the page, Karsten Bonath and I then discussed the page at length. The page did not stop evolving for several days. Karsten had several ideas, I had several requests, and we also included the idea of ​​Happy5214's table modified for convenience. The approach was as follows : We have for principle that in order to be able to observe phenomena in our project, in order to be able to notice and state conjectures, we must be able to visualize the data in all possible ways. We wanted this page to permit to do a lot of things : classify in different ways, sort, view by categories, see statistics, see sequence counters ... And so, we want to present you with a test page. It is under construction, but you can already make comments (positive or negative), suggestions, ask questions ... To access this experimental page : go to the usual page (here) and click on the "Experimental version of the page" link.
OK. Overall, the high-level design looks nice, but here comes the nit-picking:
• The document dates should be in <p> tags, likely generated by the JavaScript code.
• My CSS class name changes were made for semantic reasons. One-letter class names are categorically bad and almost never acceptable.
• (Something I missed in my own edits) <thead> and <tbody> containers should be added where appropriate. (I already see a <tfoot> in the only necessary place.)
• Fix the closing <thead> in line 125.
• The jQuery code can probably be simplified a bit, and I'm curious why Karsten used an older version (3.3.1) than my demo (3.5.1).
• The link/button table should not be a table, as it contains no tabular data and is purely for layout. It should use CSS for the same effect.
• The contributor list transclusion should probably be an iframe.
• The style attributes in the Definitions <th> tags should be replaced with scope="col" for the same effect (since that selector already has that style applied).
• Delete the empty <p> between the contributor list and the Navigation <h2>.
• Change the Navigation <section> tag to <nav>.
• Enclose the Links and statistics sections in <section> tags.
• Close the last <section>.
• Since each base is its own page now, the stats should be a separate section rather than a one-line paragraph.

I know that looks like a lot, but as I said, the design looks great.

2021-03-02, 13:17   #913
garambois

"Garambois Jean-Luc"
Oct 2011
France

22B16 Posts

Quote:
 Originally Posted by RichD Initializing base 38.

OK, many thanks !

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