1,2

The following are also members of the sequence: 1329726, 1509263, 1622441 & 1881339. - Robert G. Wilson v Mar 20 2006

2007537 is also in this sequence - Artur Jasinski (grafix(AT)csl.pl), Apr 22 2008

Author?, Title?, Mathematics Magazine, vol. 71, no. 5, page 337, Dec. 1998.

R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer-Verlag, NY, 2004, Sec. A3.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 3rd ed., Oxford Univ. Press, 1954, p. 16.

P. Ribenboim, The New Book of Prime Number Records, Springer-Verlag, NY, 1996, Chap. 2, Sec. VII.

C. K. Caldwell, Mersenne Primes

Will Edgington, List of Mersenne primes

Great Internet Mersenne Prime Search (GIMPS), Distributed Computing Projects

Andrew R. Booker, The Nth Prime Page

Pi(A000043).

The first four Mersenne numbers 2^2 - 1 = 3, 2^3 - 1 = 7, 2^5 - 1 = 31, and 2^7 - 1 = 127 are prime, so 1, 2, 3, 4 are members. But the fifth Mersenne number 2^11 - 1 = 2047 = 23*89 is composite, so 5 is not a member.

a = {}; Do[If[PrimeQ[2^Prime[n] - 1], AppendTo[a, n]], {n, 1, 100}]; a (*Artur Jasinski*)

Cf. A000043, A001348.

See also A059305 Pi(n-th Mersenne prime).

Sequence in context: A061985 A102826 A027206 this_sequence A032900 A114391 A077436

Adjacent sequences: A016024 A016025 A016026 this_sequence A016028 A016029 A016030

nonn,nice,hard

Robert G. Wilson v (rgwv(AT)rgwv.com)

Corrected by Vasiliy Danilov (danilovv(AT)usa.net) Jun 15 1998. Further corrections from Reto Keiser (rkeiser(AT)stud.ee.ethz.ch), Jan 10, 2001.

a(39) from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 20 2006