A079269 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).
1, 3, 21, 861, 1275141, 2551762438701, 9546380157472159016030421, 126857284256055227389078067834858327568823447932861
Offset: 1
Examples
The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = a(n)/A079278.
Links
- Leroy Quet, a(m) =a(m-1)+1/(1+1/a(m-1)), posting to SeqFan mailing list, Feb 15 2003.
Programs
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Maple
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
nxt[n_]:=n+1/(1+1/n); Numerator/@Nest[Append[#,nxt[Last[#]]]&,{1},10] (* Harvey P. Dale, Apr 21 2011 *)
Formula
Conjecture: a(m+1) = a(m)^2 + a(m)^3 /(2a(m-1)^2) - a(m)a(m-1)^2/2 for m >= 2. - Leroy Quet
Comments