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.

A317724 Smallest prime q < A266829(n) such that both A266829(n)^(q-1) == 1 (mod q^2) and q^(A266829(n)-1) == 1 (mod A266829(n)^2), i.e., smallest prime q less than A266829(n) such that q and A266829(n) form a double Wieferich prime pair.

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%I A317724 #11 Feb 16 2025 08:33:56
%S A317724 2,83,2903,911,3,5
%N A317724 Smallest prime q < A266829(n) such that both A266829(n)^(q-1) == 1 (mod q^2) and q^(A266829(n)-1) == 1 (mod A266829(n)^2), i.e., smallest prime q less than A266829(n) such that q and A266829(n) form a double Wieferich prime pair.
%H A317724 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleWieferichPrimePair.html">Double Wieferich Prime Pair</a>
%e A317724 a(2) = 83, because 83 is the smallest prime q such that A266829(2) = 4871 satisfies both 4871^(q-1) == 1 (mod q^2) and q^(4871-1) == 1 (mod 4871^2).
%o A317724 (PARI) forprime(p=3, , forprime(q=2, p-1, if(Mod(p, q^2)^(q-1)==1 && Mod(q, p^2)^(p-1)==1, print1(q, ", "); break)))
%Y A317724 Cf. A266829. Supersequence of A124121.
%Y A317724 Cf. A282293.
%K A317724 nonn,hard,more
%O A317724 1,1
%A A317724 _Felix Fröhlich_, Aug 05 2018