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A116945 Numbers in both A002731(n) and A002731(A002731(n)). 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 05:23 EST 2020. Contains 332086 sequences. (Running on oeis4.)