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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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OFFSET
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1,2
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REFERENCES
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LINKS
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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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MATHEMATICA
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nxt[n_]:=n+1/(1+1/n); Numerator/@Nest[Append[#, nxt[Last[#]]]&, {1}, 10] (* Harvey P. Dale, Apr 21 2011 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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The next term is too large to include.
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STATUS
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approved
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