cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

N. J. A. Sloane, Feb 16 2003

Keywords

Comments

The next term is too large to include.
The same sequence of denominators is produced by c(1) = 1 and for n > 1, c(n) = c(n-1) + 1/(n + 1 - c(n-1)). In that case, the sequence begins 1, 3/2, 19/10, 689/310, 902919/363010, 1610893922869/594665194510, ... . - Leonid Broukhis, Jul 09 2022

Examples

			The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ...
		

References

Crossrefs

Cf. A079269 (numerators), A355615 (other numerators).

Programs

  • Maple
    b := proc(n) option remember; if n=1 then 1 else b(n-1)+1/(1+1/b(n-1)); fi; end;
  • Mathematica
    Denominator[NestList[#+1/(1+1/#)&,1,10]] (* Harvey P. Dale, Oct 07 2012 *)

Formula

Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 / a(m-1)^2 - a(m)*a(m-1)^2 for m >= 2.

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

Views

Author

N. J. A. Sloane, Feb 16 2003

Keywords

Comments

The next term is too large to include.

Examples

			The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = a(n)/A079278.
		

Crossrefs

Programs

  • Maple
    b := proc(n) option remember; if n=1 then 1 else b(n-1)+1/(1+1/b(n-1)); fi; end;
  • 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

A080986 Ratios of successive terms of A080984.

Original entry on oeis.org

4, 14, 178, 29506, 824811586, 652329111297234946, 411563898885102610704583389879582466, 164866004502764290755787184747538569374756887082805069905652869331016706
Offset: 1

Views

Author

Hugo Pfoertner, Feb 26 2003

Keywords

Crossrefs

A080990 Ratios of successive terms of A080988.

Original entry on oeis.org

5, 23, 497, 235457, 53392510817, 2766001621753572646817, 7464467658097380439898886826586276934412577, 54590148152787377961058637956673631049748025019190698768473358337478050935712219773217
Offset: 1

Views

Author

Hugo Pfoertner, Feb 26 2003

Keywords

Crossrefs

Showing 1-4 of 4 results.