A079278
Define a rational sequence {b(n)} as b(1) = 1, b(n) = b(n-1) + 1/(1 + 1/b(n-1)) for n > 1; a(n) is the denominator of b(n).
Original entry on oeis.org
1, 2, 10, 310, 363010, 594665194510, 1871071000515058250871610, 21362861761506953021644584296874581450310229239910
Offset: 1
The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ...
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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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Denominator[NestList[#+1/(1+1/#)&,1,10]] (* Harvey P. Dale, Oct 07 2012 *)
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).
Original entry on oeis.org
1, 3, 21, 861, 1275141, 2551762438701, 9546380157472159016030421, 126857284256055227389078067834858327568823447932861
Offset: 1
The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = a(n)/A079278.
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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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nxt[n_]:=n+1/(1+1/n); Numerator/@Nest[Append[#,nxt[Last[#]]]&,{1},10] (* Harvey P. Dale, Apr 21 2011 *)
A080986
Ratios of successive terms of A080984.
Original entry on oeis.org
4, 14, 178, 29506, 824811586, 652329111297234946, 411563898885102610704583389879582466, 164866004502764290755787184747538569374756887082805069905652869331016706
Offset: 1
A080990
Ratios of successive terms of A080988.
Original entry on oeis.org
5, 23, 497, 235457, 53392510817, 2766001621753572646817, 7464467658097380439898886826586276934412577, 54590148152787377961058637956673631049748025019190698768473358337478050935712219773217
Offset: 1
Showing 1-4 of 4 results.
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