A116945 Numbers in both A002731(n) and A002731(A002731(n)).

3, 11, 19, 59, 69, 221, 271, 349, 371, 391, 441, 451, 521, 529, 649, 779, 869, 921, 929, 951, 1001, 1031, 1051, 1171, 1359, 1391, 1421, 1689, 1701, 2199, 2321, 2349, 2381, 2671, 2711, 2719, 2821, 2901, 3001, 3241, 3341, 3399, 3441, 3499, 3691, 4299

Offset

1,1

Comments

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

References

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

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

Crossrefs

Cf. A000040, A002731, A027861, A027862, A091277.

Cf. A002731, A188546, A188547, A187431.

Sequence in context: A163851 A213051 A238362 * A048270 A183459 A176872

Adjacent sequences: A116942 A116943 A116944 * A116946 A116947 A116948

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 25 2006

Extensions

More terms from Zak Seidov, Apr 03 2011

Status

approved