A124924 Primes p such that p^2 divides A124923((3p-1)/2) = ((3p-1)/2)^(3(p-1)/2) + 1.

5, 13, 173, 5501

Offset

1,1

Comments

p divides A124923((3p-1)/2) for primes p in A003628. Hence this sequence is a subsequence of A003628.

Also, primes p such that (-2)^((p-1)/2) == -1-3p/2 (mod p^2).

No other terms below 10^11.

Links

Table of n, a(n) for n=1..4.

Example

5 is in this sequence because A124923((3*5-1)/2) = A124923(7) = 7^8 + 1 = 117650 is divisible by 5^2 = 25.

Mathematica

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} ]

Crossrefs

Cf. A124923, A003628.

Sequence in context: A214591 A159261 A117077 * A209271 A352083 A355763

Adjacent sequences: A124921 A124922 A124923 * A124925 A124926 A124927

Keyword

hard,more,nonn

Author

Alexander Adamchuk, Nov 12 2006

Extensions

Edited by Max Alekseyev, Jan 28 2012

Status

approved