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A005849 Prime Cullen numbers: numbers n such that n*2^n + 1 is prime.
(Formerly M5401)
1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 (list; graph; refs; listen; history; text; internal format)



J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 141, p. 48, Ellipses, Paris 2008.

H. Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190-191.

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 283.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..16.

Ray Ballinger, Cullen Primes: Definition and Status

C. 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


lst={}; Do[If[PrimeQ[n*2^n+1], Print[n]; AppendTo[lst, n]], {n, 10^9}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)


Cf. A002064, A050920, A002234, A173474 (complement).

Sequence in context: A204469 A201553 A186955 * A172633 A221104 A202045

Adjacent sequences:  A005846 A005847 A005848 * A005850 A005851 A005852




N. J. A. Sloane


a(14)=1354828 from 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



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Last modified November 28 16:58 EST 2015. Contains 264588 sequences.