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A007013
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a(0) = 2; for n >= 0, a(n+1) = 2^a(n) - 1.
(Formerly M0866)
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4
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OFFSET
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0,1
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COMMENTS
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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.
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REFERENCES
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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).
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LINKS
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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.
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FORMULA
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a(n) = M(a(n-1)) = M^n(2) with M: n-> 2^n-1 - M. F. Hasler, Nov 15 2006
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MAPLE
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M:=n->2^n-1; '(M@@i)(2)'$i=0..4; - M. F. Hasler, Nov 15 2006
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MATHEMATICA
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NestList[2^#-1&, 2, 4] (* From Harvey P. Dale, Jul 18 2011 *)
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CROSSREFS
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Cf. A014221.
Sequence in context: A083436 A088856 A173913 * A103405 A087311 A053924
Adjacent sequences: A007010 A007011 A007012 * A007014 A007015 A007016
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Nik Lygeros (webmaster(AT)lygeros.org)
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EXTENSIONS
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The next term is too large to include.
Edited by Henry Bottomley, Nov 07 2002
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STATUS
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approved
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