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A255923 Bases b for which exactly two Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.

%I A255923 #15 Feb 16 2025 08:33:25
%S A255923 17,18,26,37,40,41,49,51,57,62,63,65,67,69,71,73,75,76,81,82,93,97,
%T A255923 101,109,121,124,125,127,130,134,149,157,164,165,168,172,174,179,188,
%U A255923 190,193,195,199,201,202,206,207,214,217,218,221,229,235,236,239,241
%N A255923 Bases b for which exactly two Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.
%C A255923 Numbers b such that A255920(b) = 2.
%H A255923 Felix Fröhlich, <a href="/A255923/b255923.txt">Table of n, a(n) for n = 1..10000</a>
%H A255923 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WieferichPrime.html">Wieferich Prime</a>
%o A255923 (PARI) is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 2, return(0))); i==2
%o A255923 (Sage) [b for b in range(3,242) if len([p for p in range(2,b) if is_prime(p) and mod(b, p^2)^(p-1)==1])==2] # _Danny Rorabaugh_, Mar 31 2015
%Y A255923 Cf. A255920.
%Y A255923 Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).
%K A255923 nonn
%O A255923 1,1
%A A255923 _Felix Fröhlich_, Mar 23 2015