A076339 Primes of the form 512*k+1.

7681, 10753, 11777, 12289, 13313, 15361, 17921, 18433, 19457, 23041, 25601, 26113, 32257, 36353, 37889, 39937, 40961, 45569, 50177, 51713, 58369, 59393, 61441, 64513, 65537, 67073, 70657, 76289, 76801, 79873, 80897, 81409, 83969

Offset: 1

Author

Reinhard Zumkeller, Oct 07 2002

Keywords

• nonn
• easy

Comments

Odd primes p such that -1 is a 256th power mod p. - Eric M. Schmidt, Mar 27 2014

Examples

			A076338(15) = 512*15+1 = a(1) = 7681 = A000040(974);
A076338(21) = 512*21+1 = a(2) = 10753 = A000040(1311);
a(38) - a(37) = 95233 - 87553 = 7680 = a(1)-1.
		

References

• M. Kraitchik, Theorie des Nombres, Gauthier-Villars (I. 1922, II. 1929).
• M. Kraitchik, Recherches sur la theorie des nombres, Gauthier-Villars (1924).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076338, A065091, A002144, A007519, A094407, A133870, A142925, A208177, A208178.

Programs

Haskell

a076339 n = a076339_list !! (n-1)
a076339_list = filter ((== 1) . a010051) [1,513..]
-- Reinhard Zumkeller, Mar 06 2012

Mathematica

Select[512 Range[164] + 1, PrimeQ] (* Bruno Berselli, Feb 23 2012 *)

PARI

forprimestep(p=7681,83969,512, print1(p", ")) \\ Charles R Greathouse IV, Nov 01 2022

Formula

a(n) ~ 256n log n. - Charles R Greathouse IV, Nov 01 2022