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A007013 a(0) = 2; for n >= 0, a(n+1) = 2^a(n) - 1.
(Formerly M0866)
4
2, 3, 7, 127, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Orbit of 2 under iteration of the "Mersenne operator" M: n -> 2^n-1 (0 and 1 are fixed points of M). - M. F. Hasler, Nov 15 2006

Called also the Catalan sequence - Artur Jasinski, Nov 25 2007

A180094(a(n)) = n + 1.

REFERENCES

P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 2nd ed., 1989, p. 81.

W. Sierpi\'{n}ski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 91.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..4.

Eric Weisstein's World of Mathematics, Catalan-Mersenne Number

Will Edgington, Status of M(M(p)) where M(p) is a Mersenne prime.

Eric Weisstein's World of Mathematics, Double Mersenne Number.

Chris K. Caldwell, Mersenne Primes.

FORMULA

a(n) = M(a(n-1)) = M^n(2) with M: n-> 2^n-1 - M. F. Hasler, Nov 15 2006

MAPLE

M:=n->2^n-1; '(M@@i)(2)'$i=0..4; - M. F. Hasler, Nov 15 2006

MATHEMATICA

NestList[2^#-1&, 2, 4] (* Harvey P. Dale, Jul 18 2011 *)

CROSSREFS

Cf. A014221.

Sequence in context: A083436 A088856 A173913 * A103405 A087311 A053924

Adjacent sequences:  A007010 A007011 A007012 * A007014 A007015 A007016

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nik Lygeros (webmaster(AT)lygeros.org)

EXTENSIONS

The next term is too large to include.

Edited by Henry Bottomley, Nov 07 2002

STATUS

approved

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Last modified April 24 04:54 EDT 2014. Contains 240947 sequences.