A195631 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).

4, 171, 3304, 36456, 193028, 198629, 64044140, 3209176272, 2089963197, 14714161192, 151173075361, 450458512764, 1490895165780, 4767682119956876, 19409457907183648, 293100434264580753, 818944253254104320, 19191303984466705047

Offset: 1

Author

Clark Kimberling, Sep 22 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195632, A195633.

Programs

Mathematica

r = Sqrt[2/3]; z = 28;
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}]]  (* A195631, A195632 *)
Sqrt[a^2 + b^2] (* A195633 *)
(* Peter J. C. Moses, Sep 02 2011 *)