A002254 Numbers k such that 5*2^k + 1 is prime. (Formerly M2635 N1046)

1, 3, 7, 13, 15, 25, 39, 55, 75, 85, 127, 1947, 3313, 4687, 5947, 13165, 23473, 26607, 125413, 209787, 240937, 819739, 1282755, 1320487, 1777515

Offset

1,2

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

Table of n, a(n) for n=1..25.

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.

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. [Annotated scanned copy of selected pages. The first page is (accidentally) included with the scan of the Wilson letter below.]

Eric Weisstein's World of Mathematics, Proth Prime

R. G. Wilson v, Letter (FAX) to N. J. A. Sloane, May 20 1994, concerning A002253-A002274, A000043, A002235-A002240, A001770-A001775, A007117, and many other sequences

Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Mathematica

lst={}; Do[If[PrimeQ[5*2^n+1], AppendTo[lst, n]], {n, 0, 2*10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)

Prog

(PARI) is(n)=isprime(5*2^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Crossrefs

Cf. A050526.

Sequence in context: A255682 A080565 A164344 * A356211 A331036 A060657

Adjacent sequences: A002251 A002252 A002253 * A002255 A002256 A002257

Keyword

hard,more,nonn

Author

N. J. A. Sloane

Extensions

Corrected (removed incorrect term 40937) and added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013

Status

approved