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A016027
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Indices of prime Mersenne numbers (A001348).
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4
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1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111, 207, 328, 339, 455, 583, 602, 1196, 1226, 1357, 2254, 2435, 2591, 4624, 8384, 10489, 12331, 19292, 60745, 68301, 97017, 106991, 215208, 218239, 474908, 877615, 1329726
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The following are also members of the sequence: 1329726, 1509263, 1622441, 1881339, 2007537, 2270720, 2584328, and 2610944.
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REFERENCES
| Paulo Ribenboim, "Galimatias arithmeticae", Mathematics Magazine, vol. 71, no. 5, page 337, Dec. 1998.
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.
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LINKS
| C. K. Caldwell, Mersenne Primes
Will Edgington, List of Mersenne primes
Great Internet Mersenne Prime Search (GIMPS), Distributed Computing Projects
Andrew R. Booker, The Nth Prime Page
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FORMULA
| Pi(A000043).
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EXAMPLE
| The first four Mersenne numbers 2^2 - 1 = 3, 2^3 - 1 = 7, 2^5 - 1 = 31 and 2^7 - 1 = 127 are prime, so 1, 2, 3, 4 are members. But the fifth Mersenne number 2^11 - 1 = 2047 = 23*89 is composite, so 5 is not a member.
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MATHEMATICA
| a = {}; Do[If[PrimeQ[2^Prime[n] - 1], AppendTo[a, n]], {n, 1, 100}]; a (*Artur Jasinski*)
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CROSSREFS
| Cf. A000043, A001348.
See also A059305 Pi(n-th Mersenne prime).
Sequence in context: A163866 A027206 A198034 * A205591 A191282 A191281
Adjacent sequences: A016024 A016025 A016026 * A016028 A016029 A016030
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KEYWORD
| nonn,nice,hard
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| Corrected by Vasiliy Danilov (danilovv(AT)usa.net) Jun 15 1998. Further corrections from Reto Keiser (rkeiser(AT)stud.ee.ethz.ch), Jan 10, 2001.
a(39) from Robert G. Wilson v (rgwv(at)rgwv.com), Mar 20 2006.
a(40) from Robert G. Wilson v (rgwv(at)rgwv.com), May 29 2011.
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