1,1

A124923(n) = n^(n-1) + 1 = {2,3,10,65,626,7777,117650,2097153,...}. p divides A124923[(3p-1)/2] for prime p = {5,7,13,23,29,31,37,47,53,61,71,79,101,103,109,127,149,151,157,167,173,181,191, 197,199,...} = A003628(n) Primes congruent to {5, 7} mod 8. All a(n) belong to A003628(n). p^2 divides A124923[(3p-1)/2] for p = a(n).

a(1) = 5 because A124923[(3*5-1)/2] = A124923[7] = 7^8 + 1 = 117650 is divisible by 5^2 = 25.

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} ]

Cf. A124923, A003628.

Adjacent sequences: A124921 A124922 A124923 this_sequence A124925 A124926 A124927

Sequence in context: A005764 A099974 A117077 this_sequence A124878 A085554 A067135

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 12 2006