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Search: id:A079269
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| A079269 |
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Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(1+1/b(n-1)); sequence gives numerator of b(n). |
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7
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| 1, 3, 21, 861, 1275141, 2551762438701, 9546380157472159016030421, 126857284256055227389078067834858327568823447932861
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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Suggested by Leroy Quet Feb 14 2003.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 /(2a(m-1)^2) - a(m)a(m-1)^2/2 for m >= 2.
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EXAMPLE
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The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = A079268/A079269.
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MAPLE
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b := proc(n) option remember; if n=1 then 1 else b(n-1)+1/(1+1/b(n-1)); fi; end;
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CROSSREFS
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Cf. A079278, A080581, A080582.
Sequence in context: A001699 A162924 A057600 this_sequence A127104 A144621 A111433
Adjacent sequences: A079266 A079267 A079268 this_sequence A079270 A079271 A079272
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2003
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EXTENSIONS
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The next term is too large to include.
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