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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). 7
1, 3, 21, 861, 1275141, 2551762438701, 9546380157472159016030421, 126857284256055227389078067834858327568823447932861 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Suggested by Leroy Quet, Feb 14 2003.

LINKS

Table of n, a(n) for n=1..8.

FORMULA

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

EXAMPLE

The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ... = A079268/A079269.

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 *)

CROSSREFS

Cf. A079278, A080581, A080582.

Sequence in context: A171104 A057600 A162924 * A127104 A176430 A144621

Adjacent sequences:  A079266 A079267 A079268 * A079270 A079271 A079272

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Feb 16 2003

EXTENSIONS

The next term is too large to include.

STATUS

approved

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Last modified May 21 00:57 EDT 2019. Contains 323429 sequences. (Running on oeis4.)