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.

A343410 a(n) is the smallest A (in absolute value) such that for p = prime(n), 3^{(p-1)/2} == +-1 + A*p (mod p^2), i.e., such that p is a base-3 near-Wieferich prime (near-Mirimanoff prime).

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%I A343410 #7 Apr 20 2021 10:37:47
%S A343410 1,2,3,0,4,5,9,3,7,7,9,10,1,18,15,9,24,26,16,13,27,32,12,45,8,10,49,4,
%T A343410 2,30,28,9,47,6,22,47,49,50,56,43,66,55,22,14,74,9,61,96,21,25,47,22,
%U A343410 111,64,23,5,114,128,110,121,86,56,90,156,117,48,166,133
%N A343410 a(n) is the smallest A (in absolute value) such that for p = prime(n), 3^{(p-1)/2} == +-1 + A*p (mod p^2), i.e., such that p is a base-3 near-Wieferich prime (near-Mirimanoff prime).
%C A343410 a(n) = 0 if and only if p is a base-3 Wieferich prime (Mirimanoff prime, cf. A014127).
%C A343410 These values can be used in a search for Mirimanoff primes to define "near-Mirimanoff primes" by choosing some value x and reporting all primes with |A| <= x in order to get a larger dataset.
%o A343410 (PARI) a(n) = my(p=prime(n)); abs(centerlift(Mod(3, p^2)^((p-1)/2))\/p)
%Y A343410 Cf. A014127, A258367.
%K A343410 nonn
%O A343410 2,2
%A A343410 _Felix Fröhlich_, Apr 14 2021