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Search: id:A002716
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| A002716 |
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An infinite coprime sequence defined by recursion.
(Formerly M2488 N0986)
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+0
2
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| 3, 5, 13, 17, 241, 257, 65281, 65537, 4294901761, 4294967297, 18446744069414584321, 18446744073709551617, 340282366920938463444927863358058659841
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Every term is relatively prime to all others.
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. W. F. Edwards, Infinite coprime sequences, Math. Gaz., 48 (1964), 416-422.
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FORMULA
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a(2n+1)=a(2n)+a(2n-1)-1, a(2n)=a(2n-1)^2-3*a(2n-1)+3, a(0)=3, a(1)=5.
Conjecture: a(2n+1)=A001146(n+1)+1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 15 2007
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PROGRAM
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(PARI) a(n)=if(n<2, 3*(n>=0)+2*(n>0), if(n%2, a(n-1)+a(n-2)-1, a(n-1)^2-3*a(n-1)+3))
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CROSSREFS
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Cf. A001685, A002715, A003686, A064526.
Sequence in context: A038185 A131020 A084706 this_sequence A046154 A075704 A045413
Adjacent sequences: A002713 A002714 A002715 this_sequence A002717 A002718 A002719
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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).
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EXTENSIONS
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More terms from J. O. Shallit.
Edited by Michael Somos Feb 01 2004
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