A105151 Greatest numerator among the n! ratios equal to the continued fractions which have the permutations of (1,2,3,...,n) for terms.

1, 3, 11, 48, 253, 1576, 11331, 92467, 845064, 8554195, 95032146, 1149773923, 15050556403, 211951761735, 3195468293093, 51354400809456, 876431092504915, 15830294577832786, 301703171661686235, 6050766978392127541, 127383588868883838996, 2808790552014917701633

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..175

Formula

a(n) ~ c * n!, where c = 2.61781739197011756877854274... . - Vaclav Kotesovec, Aug 25 2014

Example

a(4) = 48 because the continued fractions [4;2,1,3] (= 48/11) and [3;1,2,4] (= 48/13) have the greatest numerators among continued fraction which each have a permutation of (1,2,3,4) for terms.

Maple

r:= proc(l) local j; infinity; for j to nops(l) do l[j] +1/% od end: gl:= proc(n) local i, l; l:=[]; for i to n do l:= `if` (irem (i, 2)=0, [l[], i], [i, l[]]) od; l end: a:= n-> numer (r (gl (n))): seq (a(n), n=1..30); # Alois P. Heinz, Nov 18 2009

Mathematica

Table[Max@ Map[Numerator@ FromContinuedFraction@ # &, Permutations@ Range@ n], {n, 10}] (* Michael De Vlieger, Sep 25 2017 *)

Crossrefs

Sequence in context: A113060 A186374 A187249 * A111680 A095822 A025539

Adjacent sequences: A105148 A105149 A105150 * A105152 A105153 A105154

Keyword

nonn

Author

Leroy Quet, Apr 10 2005

Extensions

More terms from Vladeta Jovovic and David W. Wilson, Apr 12 2005

Further terms from Alois P. Heinz, Nov 18 2009

Status

approved