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A005849 Prime Cullen numbers: numbers n such that n*2^n + 1 is prime.
(Formerly M5401)
20

%I M5401

%S 1,141,4713,5795,6611,18496,32292,32469,59656,90825,262419,361275,

%T 481899,1354828,6328548,6679881

%N Prime Cullen numbers: numbers n such that n*2^n + 1 is prime.

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

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

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

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

%H Ray Ballinger, <a href="http://web.archive.org/web/20161028015144/http://www.prothsearch.net/cullen.html">Cullen Primes: Definition and Status</a>

%H Chris K. Caldwell, <a href="http://primes.utm.edu/top20/page.php?id=6">The Top Twenty: Cullen Primes</a>

%H H. Dubner, <a href="/A005849/a005849.pdf">Generalized Cullen numbers</a>, J. Rec. Math., 21 (No. 3, 1989), 190-191. (Annotated scanned copy)

%H R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/">The Top Ten: a Catalogue of Primal Configurations</a>

%H PrimeGrid, <a href="http://www.primegrid.com/primes/primes.php?project=CUL">PrimeGrid Primes: Subproject: (CUL) Cullen Prime Search</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CullenNumber.html">Cullen Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>

%t Select[Range[1000], PrimeQ[# 2^# + 1] &] (* _Alonso del Arte_, Jul 30 2017 *)

%o (PARI) is(n)=isprime(n<<n + 1) \\ _Charles R Greathouse IV_, Feb 06 2017

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

%K hard,nonn,nice,more

%O 1,2

%A _N. J. A. Sloane_

%E a(14) = 1354828 from old Proth Search pages by Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Apr 20 2006

%E 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.

%E 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.

%E Added a(16) = 6679881 from Caldwell's page, fixed broken link. - _M. F. Hasler_, Jan 18 2015

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)