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

Author

Alexander Adamchuk, Nov 12 2006

Keywords

• hard
• more
• nonn

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.

Examples

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

Crossrefs

Cf. A124923, A003628.

Programs

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} ]

Extensions

Edited by Max Alekseyev, Jan 28 2012