A002261 Numbers k such that 11*2^k + 1 is prime.
1, 3, 5, 7, 19, 21, 43, 81, 125, 127, 209, 211, 3225, 4543, 10179, 15329, 18759, 28277, 93279, 105741, 268009, 412447, 525589, 644677, 886071, 960901, 1343347, 2230369, 2476839, 2691961, 2897409, 3771821, 8103463
Offset: 1
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
- Ray Ballinger, Proth Search Page.
- Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300.
- 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.
- Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime
Programs
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Mathematica
Select[Range[1000], PrimeQ[11*2^#+1] &] (* Amiram Eldar, Dec 12 2018 *)
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PARI
is(n)=ispseudoprime(11*2^n+1) \\ Charles R Greathouse IV, Feb 20 2017
Extensions
Added more terms (from http://web.archive.org/web/20161028080239/http://www.prothsearch.net/riesel.html), Joerg Arndt, Apr 07 2013
a(30)-a(32) from http://www.prothsearch.com/riesel1.html by Robert Price, Dec 12 2018
a(33) from Jeppe Stig Nielsen, Dec 22 2024