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 *)
A080987
Ratios of successive terms of A080985.
Original entry on oeis.org
3, 11, 145, 24721, 706521601, 568754681712768961, 364030550787463437509470123011290881, 147562413614008475146723669284672702440197339884722672618106791371480321
Offset: 1
A080991
Ratios of successive terms of A080989.
Original entry on oeis.org
4, 19, 421, 203461, 46882572661, 2460798973136286293701, 6713425293781487374296340087251890561890261, 49548081347487610687284649853537701683093220643723475323834248591924587627064854208741
Offset: 1
Showing 1-4 of 4 results.
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