A080984 -id:A080984 - cp's OEIS frontend

A080986 Ratios of successive terms of A080984.

4, 14, 178, 29506, 824811586, 652329111297234946, 411563898885102610704583389879582466, 164866004502764290755787184747538569374756887082805069905652869331016706

Offset: 1

Hugo Pfoertner, Feb 26 2003

nonn

Cf. A080984, A080581.

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

N. J. A. Sloane, Feb 16 2003

The next term is too large to include.

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

Leroy Quet, a(m) =a(m-1)+1/(1+1/a(m-1)), posting to SeqFan mailing list, Feb 15 2003.

Cf. A079278, A080581, A080582, A080984, A080985.

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

nxt[n_]:=n+1/(1+1/n); Numerator/@Nest[Append[#,nxt[Last[#]]]&,{1},10]  (* Harvey P. Dale, Apr 21 2011 *)

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

A080985 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(2+1/b(n-1)); sequence gives denominator of b(n).

Original entry on oeis.org

1, 3, 33, 4785, 118289985, 83574429584465985, 47533348097639173195113266868291585, 17303590888755815609063515462865866934559547198082397287546077959536385

Offset: 1

Hugo Pfoertner, Feb 26 2003

Suggested by Leroy Quet, Feb 26 2003.

			See under A080984.

Cf. A080984, A080986, A080987, A079269, A079278.

See under A080984.

cp's OEIS Frontend

A080986 Ratios of successive terms of A080984.

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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).

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A080985 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(2+1/b(n-1)); sequence gives denominator of b(n).

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