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%I #12 Jun 12 2019 16:44:37
%S 3,11,19,59,69,221,271,349,371,391,441,451,521,529,649,779,869,921,
%T 929,951,1001,1031,1051,1171,1359,1391,1421,1689,1701,2199,2321,2349,
%U 2381,2671,2711,2719,2821,2901,3001,3241,3341,3399,3441,3499,3691,4299
%N Numbers in both A002731(n) and A002731(A002731(n)).
%C Subset of A002731. A002731(n) = 2*A027861(n-1)+1. A027862 gives primes, A091277 gives prime index.
%D L. Euler, De numeris primis valde magnis (E283), reprinted in: Opera Omnia. Teubner, Leipzig, 1911, Series (1), Vol. 3, p. 24.
%H Ray Chandler, <a href="/A116945/b116945.txt">Table of n, a(n) for n = 1..10000</a>
%F n such that (n^2 + 1)/2 is prime and (((n^2 + 1)/2)^2 + 1)/2 is prime.
%e a(1) = 3 because (3^2 + 1)/2 = 5 is prime and (5^2 + 1)/2 = 13 is prime.
%e a(2) = 11 because (11^2 + 1)/2 = 61 is prime and (61^2 + 1)/2 = 1861 is prime.
%e a(3) = 19 because (19^2 + 1)/2 = 181 is prime and (181^2 + 1)/2 = 16381 is prime.
%e a(4) = 59 because (59^2 + 1)/2 = 1741 is prime and (1741^2 + 1)/2 = 1515541 is prime.
%e 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.
%e a(6) = 221 because (221^2 + 1)/2 = 24421 is prime and (24421^2 + 1)/2 = 298192621 is prime.
%Y Cf. A000040, A002731, A027861, A027862, A091277.
%Y Cf. A002731, A188546, A188547, A187431.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 25 2006
%E More terms from _Zak Seidov_, Apr 03 2011
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