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A016027
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Indices of prime Mersenne numbers (A001348).
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11
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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, 1509263, 1622441, 1881339, 2007537, 2270720, 2584328, 2610944
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listen;
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OFFSET
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1,2
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COMMENTS
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The following are also members of the sequence: 3443958, 4350601, 4517402.
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REFERENCES
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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
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FORMULA
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EXAMPLE
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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
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a = {}; Do[If[PrimeQ[2^Prime[n] - 1], AppendTo[a, n]], {n, 1, 100}]; a (* Artur Jasinski *)
Position[Array[2^Prime[#] - 1 &, 640], _?PrimeQ][[All, 1]] (* Michael De Vlieger, Jan 31 2018 *)
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PROG
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(PARI) i=0; for(n=1, 1e3, if(isprime(n), i++; if(ispseudoprime(2^n-1), print1(i, ", ")))) \\ Felix Fröhlich, Aug 12 2014
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CROSSREFS
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KEYWORD
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nonn,nice,hard
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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