Mathematics desk
< September 13	<< Aug \| September \| Oct >>	September 15 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

September 14

What is the next prime p after 3612703 that also divides A005165(p-1)?

What is the next prime p after 3612703 that also divides A005165(p-1)? If p divides A005165(p-1), then p divides A005165(n) for all n >= p-1. Also, could you add the sequences of such primes p to OEIS (even if there are only two known such primes p)? 36.234.121.52 (talk) 13:42, 14 September 2023 (UTC)[reply]

Some details: a(n) is the alternating sum of factorials, so a(n) can be defined as a(0) = 0, a(n) = n! - a(n-1). If p (prime or not) divides a(n) with n>=p-1, then since p divides n+1!, p also divides a(n+1) = n+1!-a(n). By the same argument, if p does not divide a(n) with n>=p-1, then p does not divide a(n+1). So one only has to check that p divides a(p-1) to prove that it also divides a(n) for n>=p-1. Doing this for small p shouldn't be hard since you can do computations mod p. And searching for such p's can be done by computer. This was done in Zivkovic's 1999 paper (see the pdf). Zivkovic used assembler and 130 hours of computing time, but nowadays it could probably be accomplished handily on a laptop with Python. (I think the main contribution of the paper is the heuristic argument that such a p exists and doing the search would not be a waste of time and electricity. Zivkovic also considered the sum of factorials.) So my plan of attack would be to write a Python program to search for such p's, let it run until it reproduces Zivkovic's result, then let it continue to run until it produces another p.

Some sequences in the OEIS are finite or only have a finite number of known entries. I don't know what criteria are needed for an entry to be created, but it would have to be done by someone with an account. (I, for one, do not have one.) --RDBury (talk) 22:41, 14 September 2023 (UTC)[reply]

I have an OEIS account. Generally, you need at least three terms - more is better. You need to provide a clear definition and an example is nice. Also include published references and do a Cf. for any related sequences. Bubba73 ^{You talkin' to me?} 03:04, 15 September 2023 (UTC)[reply]

No problem, the sequence of Wieferich primes is also in OEIS, even if currently there are only two known Wieferich primes (1093 and 3511). 36.234.121.52 (talk) 23:20, 15 September 2023 (UTC)[reply]

I think the major reason why the Wieferich primes form an exception is because they've been extensively sought after throughout the years, with no other examples being found. The sequence of primes dividing A005165(p-1) has not yet been thoroughly examined. For what it's worth, I've searched through the next 30,000 primes and haven't found anything yet. GalacticShoe (talk) 03:28, 18 September 2023 (UTC)[reply]

SVG error in math

I see multiple SVG error messages (shown in red) in the English article Function (mathematics). There are no such errors in the same articles in other languages. Apparently it's a Wikipedia bug, but also maybe a browser issue (Chrome 117.0.5938.63). Can someone else look at this and fix if possible? 87.116.181.106 (talk) 19:22, 14 September 2023 (UTC)[reply]

Apparently it's fixed already, 2 min later. 87.116.181.106 (talk) 19:23, 14 September 2023 (UTC)[reply]