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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 (list; graph; refs; listen; history; text; internal format)
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), 190-191.

Paulo 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).

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

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Last modified August 18 08:45 EDT 2017. Contains 290685 sequences.