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A016027 Indices of prime Mersenne numbers (A001348). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The following are also members of the sequence: 1622441, 1881339, 2007537, 2270720, 2584328, and 2610944.

Numbers n such that A001348(n) is a Mersenne prime A000668. - Omar E. Pol, Jul 14 2012

Numbers n such that A060286(n) is a perfect number A000396.  Assuming there are no odd perfect numbers, A060286(a(n)) = A000396(n). - Omar E. Pol, Dec 13 2012

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..42.

Andrew R. Booker, The Nth Prime Page

C. K. Caldwell, Mersenne Primes

Will Edgington, List of Mersenne primes

Great Internet Mersenne Prime Search (GIMPS), Distributed Computing Projects

Paulo Ribenboim, Galimatias arithmeticae, Mathematics Magazine, vol. 71, no. 5, page 337, Dec. 1998.

Wikipedia, Mersenne Primes.

FORMULA

Pi(A000043).

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.

MATHEMATICA

a = {}; Do[If[PrimeQ[2^Prime[n] - 1], AppendTo[a, n]], {n, 1, 100}]; a (* Artur Jasinski *)

PrimePi[{* copy the terms from A000043 *}] (* Robert G. Wilson v, Jan 20 2014 *)

PROG

(PARI) i=0; for(n=1, 1e3, if(isprime(n), i++; if(ispseudoprime(2^n-1), print1(i, ", ")))) \\ Felix Fröhlich, Aug 12 2014

CROSSREFS

Cf. A000043, A001348, A059305 (index of the n-th Mersenne prime).

Sequence in context: A163866 A027206 A198034 * A205591 A191282 A191281

Adjacent sequences:  A016024 A016025 A016026 * A016028 A016029 A016030

KEYWORD

nonn,nice,hard

AUTHOR

Robert G. Wilson v

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, Mar 20 2006

a(40) from Robert G. Wilson v, May 29 2011

a(41) from Robert G. Wilson v, Jul 07 2012

a(42) from Robert G. Wilson v, Jan 20 2014

STATUS

approved

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Last modified December 21 09:07 EST 2014. Contains 252300 sequences.