1,1

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

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: Conjectures and Unsolved Problems

Eric Weisstein's World of Mathematics, Double Mersenne Number

Wikipedia, Mersenne prime

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

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

Sequence in context: A002357 A105765 A061095 this_sequence A089162 A016047 A003260

Adjacent sequences: A103898 A103899 A103900 this_sequence A103902 A103903 A103904

nonn

Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Feb 20 2005