1,1

Mersenne primes are solutions to sigma(n+1)-sigma(n)=n as perfect numbers (A000396(n)) are solutions to sigma(n)=2n - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 07 2002

Mersenne numbers A000225 whose indices are primes. [From Omar E. Pol (info(AT)polprimos.com), Aug 31 2008]

G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

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

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).

K. Zsigmondy, Zur Theorie der Potenreste, Monatsh. Math., 3 (1892), 265-284.

T. D. Noe, Table of n, a(n) for n=1..100

R. C. Archibald, Mersenne's Numbers

John Brillhart et al., Cunningham Project [Factorizations of b^n +- 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers]

C. K. Caldwell, Mersenne primes

Will Edgington, Mersenne Page

P. Garrett, Lucas-Lehmer criterion for primality of Mersenne numbers

Thesaurus.maths.org, Mersenne Number

G. Villemin's Almanach of Numbers, Nombre de Mersenne

E. Wegrzynowski, Nombres de Mersenne

a(n) = A000225(A000040(n)). [From Omar E. Pol (info(AT)polprimos.com), Aug 31 2008]

lst={}; Do[AppendTo[lst, 2^Prime[n]-1], {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 26 2008]

Cf. A000043, A000668, A046051, A057951-A057958, A100105.

Cf. A000040, A000225. [From Omar E. Pol (info(AT)polprimos.com), Aug 31 2008]

Sequence in context: A138864 A105768 A084924 this_sequence A006515 A093535 A081093

Adjacent sequences: A001345 A001346 A001347 this_sequence A001349 A001350 A001351

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).