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Primes of the form 512*k+1.
10

%I #29 Nov 01 2022 12:21:42

%S 7681,10753,11777,12289,13313,15361,17921,18433,19457,23041,25601,

%T 26113,32257,36353,37889,39937,40961,45569,50177,51713,58369,59393,

%U 61441,64513,65537,67073,70657,76289,76801,79873,80897,81409,83969

%N Primes of the form 512*k+1.

%C Odd primes p such that -1 is a 256th power mod p. - _Eric M. Schmidt_, Mar 27 2014

%D M. Kraitchik, Theorie des Nombres, Gauthier-Villars (I. 1922, II. 1929).

%D M. Kraitchik, Recherches sur la theorie des nombres, Gauthier-Villars (1924).

%H Reinhard Zumkeller, <a href="/A076339/b076339.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ 256n log n. - _Charles R Greathouse IV_, Nov 01 2022

%e A076338(15) = 512*15+1 = a(1) = 7681 = A000040(974);

%e A076338(21) = 512*21+1 = a(2) = 10753 = A000040(1311);

%e a(38) - a(37) = 95233 - 87553 = 7680 = a(1)-1.

%t Select[512 Range[164] + 1, PrimeQ] (* _Bruno Berselli_, Feb 23 2012 *)

%o (Haskell)

%o a076339 n = a076339_list !! (n-1)

%o a076339_list = filter ((== 1) . a010051) [1,513..]

%o -- _Reinhard Zumkeller_, Mar 06 2012

%o (PARI) forprimestep(p=7681,83969,512, print1(p", ")) \\ _Charles R Greathouse IV_, Nov 01 2022

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

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Oct 07 2002