

A002254


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


12



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
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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. 381384.
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), 673681.
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), 673681. [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 A002253A002274, A000043, A002235A002240, A001770A001775, A007117, and many other sequences
Index entries for sequences of n such that k*2^n1 (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 * A060657 A192148 A151875
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



