A002234 Numbers k such that the Woodall number k*2^k - 1 is prime.

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

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• nice
• hard

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.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 241-242.
• 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

• 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.

Crossrefs

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

Programs

PARI

is(n)=isprime(n<Charles R Greathouse IV, Feb 07 2017

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