cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A178900 First nonzero value of (a^(p-1) - 1) mod p^2, for a > 0 coprime to the n-th Wieferich prime p.

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%I A178900 #7 Sep 07 2023 07:14:43
%S A178900 341016,24577
%N A178900 First nonzero value of (a^(p-1) - 1) mod p^2, for a > 0 coprime to the n-th Wieferich prime p.
%C A178900 It is believed that a(n) = (3^(p-1) - 1) mod p^2 for all n, where p = A001220(n).
%C A178900 See additional comments, references, links and cross-references in A001220.
%H A178900 A. Ostafe and I. Shparlinski (2010), <a href="http://arxiv.org/abs/1001.1504">Pseudorandomness and Dynamics of Fermat Quotients</a>, arXiv:1001.1504 [math.NT], 2010.
%F A178900 a(n) = (A178815(A000720(p))^(p-1) - 1) mod p^2, where p = A001220(n).
%F A178900 a(n) mod p = A178844(A000720(p)), where p = A001220(n).
%e A178900 The first Wieferich prime is 1093 and a^1092 - 1 mod 1093^2 = 0, 0, 341016 for a = 1, 2, 3, so a(1) = 341016.
%Y A178900 Cf. A001220, A178815, A178844.
%K A178900 bref,hard,more,nonn
%O A178900 1,1
%A A178900 _Jonathan Sondow_, Jun 23 2010