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A001348 Mersenne numbers: 2^p - 1, where p is prime.
(Formerly M2694 N1079)
87
3, 7, 31, 127, 2047, 8191, 131071, 524287, 8388607, 536870911, 2147483647, 137438953471, 2199023255551, 8796093022207, 140737488355327, 9007199254740991, 576460752303423487, 2305843009213693951, 147573952589676412927, 2361183241434822606847 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Mersenne numbers A000225 whose indices are primes. - Omar E. Pol, Aug 31 2008

All terms are of the form 4k-1. - Paul Muljadi, Jan 31 2011

REFERENCES

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 16.

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.

LINKS

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

G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

P. Garrett, Lucas-Lehmer criterion for primality of Mersenne numbers

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

Thesaurus.maths.org, Mersenne Number

G. Villemin's Almanach of Numbers, Nombre de Mersenne

E. Wegrzynowski, Nombres de Mersenne

FORMULA

a(n) = 2^A000040(n) - 1, n >= 1. (See NAME).

a(n) = A000225(A000040(n)). - Omar E. Pol, Aug 31 2008

A000668(n) = a(A016027(n)). - Omar E. Pol, Jun 29 2012

MAPLE

A001348 := n -> 2^(ithprime(n))-1: seq (A001348(n), n=1..18);

MATHEMATICA

Table[2^Prime[n]-1, {n, 20}] (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)

PROG

(PARI) a(n)=1<<prime(n)-1 \\ Charles R Greathouse IV, Jun 10 2011

CROSSREFS

Cf. A000043, A000668, A046051, A057951-A057958, A100105.

Cf. A000040, A000225. - 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

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited: Formula according to Name added. - Wolfdieter Lang, Oct 26 2014

STATUS

approved

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Last modified April 1 05:15 EDT 2015. Contains 256111 sequences.