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Search: id:A080988
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| A080988 |
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Define b by b(1) = 1, and for n>1, b(n) = b(n-1)+1/(3+1/b(n-1)); sequence gives numerator of b(n). |
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3
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| 1, 5, 115, 57155, 13457544835, 718532108172999980195, 1987460976488531436231264449305834729789315, 14835338180729281137836887250133924105479472089418750626398379615457041439472496214755
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Suggested by Leroy Quet (qq-quet(AT)mindspring.com), Feb 26 2003.
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FORMULA
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b[k]=n[k]/d[k]; n[1]=1, d[1]=1, m=3; for k>=2: n[k+1] = n[k] *(m*n[k] + 2*d[k]), d[k+1] = d[k] *(m*n[k] + d[k])
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EXAMPLE
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The sequence begins 1, 5/4, 115/76, 57155/31996, 13457544835/6509938156, ...
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PROGRAM
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Reduce: a := 1; for i := 1:8 do write a := a+1/(3+1/a);
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CROSSREFS
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Cf. A080989, A080990, A080991, A079269, A079278.
Adjacent sequences: A080985 A080986 A080987 this_sequence A080989 A080990 A080991
Sequence in context: A091026 A089638 A109057 this_sequence A006221 A067359 A065818
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KEYWORD
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frac,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 26 2003
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