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Search: id:A064847
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| A064847 |
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Sequence is a(m), where a(1) = b(1) = 1, a(n+1) = a(n) * b(n), b(n+1) = a(n) + b(n). |
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6
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| 1, 1, 2, 6, 30, 330, 13530, 5019630, 69777876630, 351229105131280530, 24509789089304573335878465330, 8608552999157278550998626549630446732052243030
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Consider the mapping f(a/b) = (a + b)/(ab). Taking a = 1 b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 1/1, 2/1, 3/2, 5/6, 11/30, ... Sequence contains the denominators. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 24 2003
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,18
Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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a(n+2) = a(n+1)*(a(n+1)/a(n) + a(n)).
lim n -> infinity a(n)/A003686(n)^PHI=1 where PHI=(1+sqrt(5))/2 is the golden ratio. - Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2002
Denominator of b(n) where b(n) = 1/numer(b(n-1)) + 1/denom(b(n-1)), b(1)=1. Cf. A003686. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 15 2002
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PROGRAM
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(PARI) { for (n=1, 18, if (n>2, a=a1*(a1/a2 + a2); a2=a1; a1=a, a=a1=a2=1); write("b064847.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 28 2009]
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CROSSREFS
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The b(n) sequence is A003686.
See A094303 for another version.
Sequence in context: A120295 A071350 A038696 this_sequence A127815 A054934 A001684
Adjacent sequences: A064844 A064845 A064846 this_sequence A064848 A064849 A064850
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet Oct 31 2001
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