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Search: id:A007013
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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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+0
3
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| 2, 3, 7, 127, 170141183460469231731687303715884105727
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (Maximilian.Hasler(AT)gmail.com), Nov 15 2006
Called also the Catalan sequence - Artur Jasinski (grafix(AT)csl.pl), Nov 25 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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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 (Maximilian.Hasler(AT)gmail.com), 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 (Maximilian.Hasler(AT)gmail.com), Nov 15 2006
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CROSSREFS
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Cf. A014221. [From Ivor C. Quence (Ivan(AT)email_address.too), May 07 2009]
Adjacent sequences: A007010 A007011 A007012 this_sequence A007014 A007015 A007016
Sequence in context: A062935 A083436 A088856 this_sequence A103405 A087311 A053924
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), 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 (se16(AT)btinternet.com), Nov 07 2002
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