A103901 Mersenne primes p such that M(p) = 2^p - 1 is also a (Mersenne) prime.

3, 7, 31, 127

Offset

1,1

Comments

Same as exponents of double Mersenne primes. Only four terms are known.

References

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.

Links

Table of n, a(n) for n=1..4.

C. K. Caldwell, Mersenne Primes: Conjectures and Unsolved Problems

Eric Weisstein's World of Mathematics, Double Mersenne Number

Wikipedia, Mersenne prime

Example

2^2 - 1 = 3 and 2^3 - 1 = 7 are Mersenne primes, so 3 is a member.

Crossrefs

Cf. A000043, A000668, A001348, A077586, A103902.

Sequence in context: A105765 A061095 A357296 * A089162 A016047 A003260

Adjacent sequences: A103898 A103899 A103900 * A103902 A103903 A103904

Keyword

nonn,more,hard

Author

Jonathan Sondow, Feb 20 2005

Status

approved