

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
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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., SpringerVerlag, 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, SpringerVerlag, 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^n1), print1(i, ", ")))) \\ Felix FrÃ¶hlich, Aug 12 2014


CROSSREFS

Cf. A000043, A001348, A059305 (index of the nth 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



