A195565 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/4.

4, 3, 204, 280, 2280, 12596, 12797, 831996, 1149440, 9341440, 51622404, 52441603, 3409523404, 4710402840, 38281220840, 211548594996, 214905676797, 13972226073596, 19303229690880, 156876433658880, 866926090675204, 880683411072003

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195566, A195567.

Programs

Mathematica

r = 5/4; z = 26;
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}]]  (* A195565, A195566 *)
Sqrt[a^2 + b^2] (* A195567 *)
(* by Peter J. C. Moses, Sep 02 2011 *)