A195553 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/2.

5, 260, 7020, 94635, 5103280, 137599280, 1855038645, 100034487540, 2697221086300, 36362467421275, 1960876019662560, 52870927596046560, 712777084536797285, 38437091637391006820, 1036375920040483589580, 13971856374727832955915

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn
• frac

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195554, A195555.

Programs

Mathematica

r = 5/2; 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}]]  (* A195553, A195554 *)
Sqrt[a^2 + b^2] (* A195555 *)
(* Peter J. C. Moses, Sep 02 2011 *)