A002234 Numbers k such that the Woodall number k*2^k - 1 is prime. (Formerly M0820 N0311)

2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, 15822, 18885, 22971, 23005, 98726, 143018, 151023, 667071, 1195203, 1268979, 1467763, 2013992, 2367906, 3752948, 17016602

Offset

1,1

Comments

a(34) = 17016602 is tentative until the range 16838832..17016601 is fully searched. - Eric W. Weisstein, Mar 22 2018

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 115, p. 40, Ellipses, Paris 2008.

R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.

F. Le Lionnais, Les Nombres Remarquables, Paris, Hermann, 1983, p. 95, 1983.

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).

David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 139.

Links

Table of n, a(n) for n=1..34.

Ray Ballinger, Woodall Primes: Definition and Status.

Ray Ballinger and Wilfrid Keller, Woodall numbers.

C. K. Caldwell, Woodall Numbers.

J. DeMaio, Generalized Woodall Numbers.

Brady Haran and Matt Parker, 383 is cool, Numberphile video (2017).

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations.

PrimeGrid, PrimeGrid Primes: Subproject: (WOO) Woodall Prime Search.

Matt Parker and Brady Haran, 383 and Woodall Primes, Numberphile video (2017).

H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.

Eric Weisstein's World of Mathematics, Woodall Number.

Eric Weisstein's World of Mathematics, Integer Sequence Primes.

Prog

(PARI) is(n)=isprime(n<<n - 1) \\ Charles R Greathouse IV, Feb 07 2017

Crossrefs

Cf. A050918 (for the actual primes), A003261, A005849.

Sequence in context: A330030 A192441 A108326 * A074005 A145499 A221310

Adjacent sequences: A002231 A002232 A002233 * A002235 A002236 A002237

Keyword

nonn,nice,hard

Author

N. J. A. Sloane, Simon Plouffe

Extensions

a(27) communicated by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004

a(28) = 1195203 found by M. Rodenkirch; contributed by Eric W. Weisstein, Nov 29 2005

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(30)-a(33) from John Blazek, May 14 2009

a(34) = 17016602 communicated by Eric W. Weisstein, Mar 22 2018

Status

approved