%I A001348 M2694 N1079
%S A001348 3,7,31,127,2047,8191,131071,524287,8388607,536870911,2147483647,
%T A001348 137438953471,2199023255551,8796093022207,140737488355327,
%U A001348 9007199254740991,576460752303423487,2305843009213693951
%N A001348 Mersenne numbers: 2^p - 1, where p is prime.
%C A001348 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
%C A001348 Mersenne numbers A000225 whose indices are primes. [From Omar E. Pol 
               (info(AT)polprimos.com), Aug 31 2008]
%D A001348 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001348 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001348 G. Everest et al., Primes generated by recurrence sequences, Amer. Math. 
               Monthly, 114 (No. 5, 2007), 417-431.
%D A001348 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 16.
%D A001348 K. Zsigmondy, Zur Theorie der Potenreste, Monatsh. Math., 3 (1892), 265-284.
%H A001348 T. D. Noe, <a href="b001348.txt">Table of n, a(n) for n=1..100</a>
%H A001348 R. C. Archibald, <a href="http://desmatron.altervista.org/desmath/mersenne_numbers.htm">
               Mersenne's Numbers</a>
%H A001348 John Brillhart et al., <a href="http://www.ams.org/online_bks/conm22">
               Cunningham Project</a> [Factorizations of b^n +- 1, b = 2, 3, 5, 
               6, 7, 10, 11, 12 up to high powers]
%H A001348 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/mersenne/
               index.html">Mersenne primes</a>
%H A001348 Will Edgington, <a href="http://www.garlic.com/~wedgingt/mersenne.html">
               Mersenne Page</a>
%H A001348 P. Garrett, <a href="http://www.math.umn.edu/~garrett/m/number_theory/
               lucas_lehmer.pdf">Lucas-Lehmer criterion for primality of Mersenne 
               numbers</a>
%H A001348 Thesaurus.maths.org, <a href="http://thesaurus.maths.org/dictionary/map/
               word/3371">Mersenne Number</a>
%H A001348 G. Villemin's Almanach of Numbers, <a href="http://membres.lycos.fr/villemingerard/
               Decompos/Mersenne.htm">Nombre de Mersenne</a>
%H A001348 E. Wegrzynowski, <a href="http://www.lifl.fr/~wegrzyno/Mersenne/mersenne1.html">
               Nombres de Mersenne</a>
%F A001348 a(n) = A000225(A000040(n)). [From Omar E. Pol (info(AT)polprimos.com), 
               Aug 31 2008]
%t A001348 lst={};Do[AppendTo[lst, 2^Prime[n]-1], {n, 4!}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Aug 26 2008]
%Y A001348 Cf. A000043, A000668, A046051, A057951-A057958, A100105.
%Y A001348 Cf. A000040, A000225. [From Omar E. Pol (info(AT)polprimos.com), Aug 
               31 2008]
%Y A001348 Sequence in context: A138864 A105768 A084924 this_sequence A006515 A093535 
               A081093
%Y A001348 Adjacent sequences: A001345 A001346 A001347 this_sequence A001349 A001350 
               A001351
%K A001348 nonn,nice,easy
%O A001348 1,1
%A A001348 N. J. A. Sloane (njas(AT)research.att.com).