

A005849


Prime Cullen numbers: numbers n such that n*2^n + 1 is prime.
(Formerly M5401)


15



1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881
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OFFSET

1,2


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 141, p. 48, Ellipses, Paris 2008.
Harvey Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190191.
Paulo Ribenboim, The Book of Prime Number Records. SpringerVerlag, NY, 2nd ed., 1989, p. 283.
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..16.
Ray Ballinger, Cullen Primes: Definition and Status
Chris K. Caldwell, The Top Twenty: Cullen Primes
R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations
PrimeGrid, PrimeGrid Primes: Subproject: (CUL) Cullen Prime Search
Eric Weisstein's World of Mathematics, Cullen Number
Eric Weisstein's World of Mathematics, Integer Sequence Primes


MATHEMATICA

Select[Range[1000], PrimeQ[# 2^# + 1] &] (* Alonso del Arte, Jul 30 2017 *)


PROG

(PARI) is(n)=isprime(n<<n + 1) \\ Charles R Greathouse IV, Feb 06 2017


CROSSREFS

Cf. A002064, A050920, A002234, A173474 (complement).
Sequence in context: A201553 A281560 A186955 * A172633 A221104 A202045
Adjacent sequences: A005846 A005847 A005848 * A005850 A005851 A005852


KEYWORD

hard,nonn,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(14) = 1354828 from http://web.archive.org/web/20161028015144/http://www.prothsearch.net/cullen.html  Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 20 2006
The term 1467763 was added in error and has now been deleted; Jens Kruse Andersen, Nov 28 2007, remarks that 1467763 * 2^1467763  1 is a Woodall prime, but 3 divides the Cullen number 1467763 * 2^1467763 + 1.
6328548 from John Blazek, May 14 2009. He later reports that the search of the range from 6300000 to 6328548 was completed on May 28 2009.
Added a(16) = 6679881 from Caldwell's page, fixed broken link.  M. F. Hasler, Jan 18 2015


STATUS

approved



