A002256 Numbers k such that 9*2^k + 1 is prime.

1, 2, 3, 6, 7, 11, 14, 17, 33, 42, 43, 63, 65, 67, 81, 134, 162, 206, 211, 366, 663, 782, 1305, 1411, 1494, 2297, 2826, 3230, 3354, 3417, 3690, 4842, 5802, 6937, 7967, 9431, 13903, 22603, 24422, 39186, 43963, 47003, 49902, 67943, 114854, 127003, 145247

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Chap. 4, see pp. 381-384.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..60
• Ray Ballinger, Proth Search Page
• Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
• C. K. Caldwell, The Prime Pages
• Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
• Wilfrid Keller, List of primes k.2^n - 1 for k < 300
• R. M. Robinson, A report on primes of the form k.2^n+1 and on factors of Fermat numbers, Proc. Amer. Math. Soc., 9 (1958), 673-681.
• Eric Weisstein's World of Mathematics, Proth Prime
• Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Crossrefs

Cf. A050528.

Programs

Mathematica

Select[Range[2019],PrimeQ[9*2^#+1]&] (* Metin Sariyar, Sep 21 2019 *)

Extensions

a(48) from Arkadiusz Wesolowski, Oct 22 2011

Added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013

Terms moved from Data to b-file, and more terms put in b-file, by Jeppe Stig Nielsen, Sep 21 2019