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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 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 A327037 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 September 19 15:09 EDT 2020. Contains 337178 sequences. (Running on oeis4.)