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%I #9 Aug 23 2013 21:21:50
%S 5,13,173,5501
%N Primes p such that p^2 divides A124923((3p-1)/2) = ((3p-1)/2)^(3(p-1)/2) + 1.
%C p divides A124923((3p-1)/2) for primes p in A003628. Hence this sequence is a subsequence of A003628.
%C Also, primes p such that (-2)^((p-1)/2) == -1-3p/2 (mod p^2).
%C No other terms below 10^11.
%e 5 is in this sequence because A124923((3*5-1)/2) = A124923(7) = 7^8 + 1 = 117650 is divisible by 5^2 = 25.
%t Do[ p = Prime[n]; m = (3p-1)/2; f = PowerMod[ m, m-1, p^2 ] + 1; If[ IntegerQ[ f/p^2 ], Print[p] ], {n,2,10000} ]
%Y Cf. A124923, A003628.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Nov 12 2006
%E Edited by _Max Alekseyev_, Jan 28 2012
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