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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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).