1,1

Subset of A002731. A002731(n) = 2*A027861(n-1)+1. A027862 gives primes, A091277 gives prime index.

L. Euler, De numeris primis valde magnis (E283), reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 3, p. 24.

n such that (n^2 + 1)/2 is prime and (((n^2 + 1)/2)^2 + 1)/2 is prime.

a(1) = 3 because (3^2 + 1)/2 = 5 is prime, and (5^2 + 1)/2 = 13 is prime.

a(2) = 11 because (11^2 + 1)/2 = 61 is prime, and (61^2 + 1)/2 = 1861 is prime.

a(3) = 19 because (19^2 + 1)/2 = 181 is prime, and (181^2 + 1)/2 = 16381 is prime.

a(4) = 59 because (59^2 + 1)/2 = 1741 is prime, and (1741^2 + 1)/2 = 1515541 is prime.

a(5) = 69 because (69^2 + 1)/2 = 2381 is prime, and (2381^2 + 1)/2 = 2834581 is prime. Further, (2834581^2+1)/2 = 4017424722781 is prime, which suggests another sequences one level of recursion deeper.

a(6) = 221 because (221^2 + 1)/2 = 24421 is prime, and (24421^2 + 1)/2 = 298192621 is prime.

Cf. A000040, A027861, A027862, A091277.

Sequence in context: A138726 A079544 A007520 this_sequence A048270 A088733 A128996

Adjacent sequences: A116942 A116943 A116944 this_sequence A116946 A116947 A116948

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Mar 25 2006