1,2

a(1) = 1 because such a prime does not exist, Mod[n^2+1, n+1] = 2 for n>1. a(n) = (A103795[n]^Prime[n]+1)/(A103795[n]+1) when A103795[n] is prime. Corresponding smallest primes q such that (q^p+1)/(q+1) is prime, where p = Prime[n], are listed in A123627[n] = {0, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 19, 61, 2, 7, 839, 1459, 2, 5, 409, 571, 2, ...}. All Wagstaff primes or primes of form (2^p + 1)/3 belong to a(n). Wagstaff primes are listed in A000979[n] = {3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, ...}. Corresponding indices n such that a(n) = (2^Prime[n] + 1)/3 are PrimePi[A000978[n]] = {2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 22, 26, 31, 39, 43, 46, 65, 69, 126, 267, 380, 495, 762, 1285, 1304, 1364, 1479, 1697, 4469, 8135, 9193, 11065, 11902, 12923, 13103, 23396, 23642, 31850, ...}. All primes with prime indices in the Jacobsthal sequence A001045[n] belong to a(n).

a(n) = (A123627[n]^Prime[n] + 1) / (A123627[n] + 1).

Cf. A123627, A103795, A123487, A123488, A000978, A000979, A001045, A049883, A107036.

Adjacent sequences: A123625 A123626 A123627 this_sequence A123629 A123630 A123631

Sequence in context: A135482 A126614 A000979 this_sequence A107290 A122393 A012880

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 03 2006