A195535 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(6).

5, 1020, 2247, 2633277900, 2640162496, 638843546289, 1396487515808, 6103353023795, 21860678072520, 82495605773137, 29466852345019792, 34041728665663572, 292320946605948260, 262936589866701605, 3964118460886936896

Offset: 1

Author

Clark Kimberling, Sep 20 2011

Keywords

• nonn
• frac

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195536, A195537.

Programs

Mathematica

r = Sqrt[6]; z = 18;
p[{f_, n_}] := (#1[[2]]/#1[[
      1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
         2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
     Array[FromContinuedFraction[
        ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
{a, b} = ({Denominator[#1], Numerator[#1]} &)[
  p[{r, z}]]  (* A195535, A195536 *)
Sqrt[a^2 + b^2] (* A195537 *)
(* Peter J. C. Moses, Sep 02 2011 *)