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A255925 Bases b for which exactly four Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.

%I A255925 #18 Feb 16 2025 08:33:25
%S A255925 116,117,118,233,245,249,251,261,269,276,298,325,369,374,401,423,460,
%T A255925 485,487,505,526,604,618,629,653,717,721,723,737,776,793,838,851,856,
%U A255925 857,863,867,881,893,932,962,969,978,1025,1037,1045,1057,1059,1079,1106
%N A255925 Bases b for which exactly four Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.
%C A255925 Numbers b such that A255920(b) = 4.
%H A255925 Felix Fröhlich, <a href="/A255925/b255925.txt">Table of n, a(n) for n = 1..10000</a>
%H A255925 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WieferichPrime.html">Wieferich Prime</a>
%t A255925 wp[b_] := Count[Complement[Prime[Range[PrimePi[b]]], FactorInteger[b][[All, 1]] ], p_ /; Divisible[b^(p - 1) - 1, p^2]];
%t A255925 Select[Range[2, 1200], wp[#] == 4&] (* _Jean-François Alcover_, Nov 26 2017 *)
%o A255925 (PARI) is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 4, return(0))); i==4
%o A255925 (Sage) [b for b in range(3,1107) if len([p for p in range(2,b) if is_prime(p) and mod(b, p^2)^(p-1)==1])==4] # _Danny Rorabaugh_, Mar 31 2015
%Y A255925 Cf. A255920.
%Y A255925 Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).
%K A255925 nonn
%O A255925 1,1
%A A255925 _Felix Fröhlich_, Mar 23 2015