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A001348
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Mersenne numbers: 2^p - 1, where p is prime.
(Formerly M2694 N1079)
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71
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3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 536870911, 2147483647, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 2305843009213693951, 147573952589676412927, 2361183241434822606847
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OFFSET
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1,1
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COMMENTS
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Mersenne numbers A000225 whose indices are primes. [From Omar E. Pol, Aug 31 2008]
All terms are of the form 4k-1. [Paul Muljadi, Jan 31 2011]
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REFERENCES
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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.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, Arxiv preprint arXiv:1202.3670, 2012 - From N. J. A. Sloane, Jun 13 2012
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.
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LINKS
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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
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FORMULA
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a(n) = A000225(A000040(n)). [From Omar E. Pol, Aug 31 2008]
A000668(n) = a(A016027(n)). - Omar E. Pol, Jun 29 2012
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MAPLE
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A001348 := n -> 2^(ithprime(n))-1: seq (A001348(n), n=1..18);
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MATHEMATICA
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Table[2^Prime[n]-1, {n, 20}] [From Vladimir Joseph Stephan Orlovsky, Aug 26 2008]
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PROG
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(PARI) a(n)=1<<prime(n)-1 \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
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Cf. A000043, A000668, A046051, A057951-A057958, A100105.
Cf. A000040, A000225. [From Omar E. Pol, Aug 31 2008]
Cf. A002145, A045326.
Sequence in context: A138864 A105768 A084924 * A006515 A093535 A081093
Adjacent sequences: A001345 A001346 A001347 * A001349 A001350 A001351
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KEYWORD
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nonn,nice,easy,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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