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User talk:Frank Ellermann

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Edit request

Frank, I have an edit request to make of you. Could you choose the Sequence of the Day for July 4? Choose a sequence, preferably one with an A-number less than 100000, and write a couple of sentences on what it is about that particular sequence you find interesting. If you agree to this, the deadline is April 4. Alonso del Arte 01:24, 22 March 2011 (UTC)

Hi, I haven't touched any sequence for about eight years, and looking today at old sequences I'm often lost. I vaguely recall A060851, because I use it in a homebrewn REXX math package for a quick plausibility check of Euler's constant C0 against a formula based on hardwired odd zetas (from a file published by S. Plouffe, decimal precision 2000 digits). That's clearly "original research" and would violate Wikipedia policy WP:NOR, besides this sequence might be only interesting for me: WP:NOT, Wikipedia:Notability. And in the worst case this sequence does not really do what it apparently does up to a precision of 2000 digits. -Frank Ellermann 14:14, 22 March 2011 (UTC)
That's perfect! It shows that that sequence has a direct application to your mathematical research on a topic that is of interest to many people. You had me at "Euler's constant C0."
As you yourself have said, this is not Wikipedia. We don't care about what Wikipedia defines as "original research." Rather, use your commonsense to make that determination: using some simple congruences to prove an obvious fact anyone else could have done, but if it could win you a Fields medal, maybe get an ArXiV preprint first. As for "notability," well, this has to do with Riemann's zeta function, so among mathematicians, that's enough for notability. Alonso del Arte 14:49, 22 March 2011 (UTC)
JFTR, Plouffe's file offers only 1000 decimal digits limiting RxShell to NUMERIC DIGITS 500 for internal uses of double precision in some supported functions.
Frank Ellermann 08:46, 21 April 2011 (UTC)

Sequence of the Day for July 4

So, Frank, do you still plan to write the Sequence of the Day for July 4? If you can't do it by tomorrow, I will. July 10 is available, though. Alonso del Arte 23:38, 3 April 2011 (UTC)

Done, I used your July 4 proposal as example. After all I think A060851 actually is interesting enough, only the link to my own RxShell is odd. OTOH I used RxShell when I helped to edit OEIS years ago, and the odd zeta values plus C0 were required to check or create some published sequences. –Frank Ellermann 19:07, 20 April 2011 (UTC)
Thanks very much, Frank. I think I will ask Charles to review this one. But of much more immediate concern, could you review the Sequence of the Day for July 2? I was going to ask Daniel to review it but since I based it practically word for word on something he wrote, I think someone else should look at it. Alonso del Arte 23:39, 20 April 2011 (UTC)
Okay, but I have no idea what a review is, apart from adding a checkmark.  Some thoughts; ignoring 1, 2, and 3 all primes have either the form 5+6*n or 7+6*n for 0 <= n.  Therefore p²-q² is
  1. (5+6n)*(5+6n)-(5+6m)*(5+6m)=25+30n+30n+36n²-25-30m-30m-36m²=60(n-m)+36(n²-m²)=12*(5(n-m)+3(n²-m²))
  2. (7+6n)*(7+6n)-(5+6m)*(5+6m)=49+42n+42n+36n²-25-30m-30m-36m²=24+84n-60m+36(n²+m²)=12*(2+7n-5m+3(n²-m²))
  3. (5+6n)*(5+6n)-(7+6m)*(7+6m) — ditto swapping n and m
  4. (7+6n)*(7+6n)-(7+6m)*(7+6m)=49+42n+42n+36n²-49-42m-42m-36m²=84(n-m)+36(n²+m²)=12*(7(n-m)+3(n²-m²))
You need 2*12 instead of 12, that should be obvious, but I don't see it at the moment.  As you write (7+6n) can be transformed into (1+6n) to include 1, and after that q=1 is a special case where p²-1 still has the form 24*k for p=1, 5, 7, 11, 13, and so on.  In theory the sequence could start at 0 if it would permit prime(0)=1 — not an unusual definition, especially for cases where it works… :-)  Now please tell me where the missing 2 for 2*12 is, and I can add a checkmark to your proposal. –Frank Ellermann 08:32, 21 April 2011 (UTC)