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%I #16 Mar 03 2018 23:36:53
%S 29,37,3373
%N Primes p such that p^2 divides Sierpinski number A014566((p-1)/2).
%C Subsequence of A003628.
%C No other terms below 10^11. - _Max Alekseyev_, Sep 18 2010
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiNumberoftheFirstKind.html">Sierpinski Number of the First Kind</a>.
%F Elements of A125854 that are congruent to 5 or 7 modulo 8, i.e., primes p such that p == 5 or 7 (mod 8) and 2^(p-1) == 1+p (mod p^2). - _Max Alekseyev_, Sep 18 2010
%t Do[p=Prime[n];f=((p-1)/2)^((p-1)/2)+1;If[IntegerQ[f/p^2],Print[p]],{n,1,3373}]
%o (PARI) { forprime(p=3, 10^11, if(Mod((p-1)/2, p^2)^((p-1)/2)==-1, print(p); )) } \\ _Max Alekseyev_, Sep 18 2010
%Y Cf. A014566, A003628.
%K bref,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Sep 11 2006
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