A195550 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2.

3, 60, 660, 3597, 78480, 856080, 4669203, 101866380, 1111191780, 6060621597, 132222483360, 1442326073760, 7866682164003, 171624681534300, 1872138132549300, 10210947388253997, 222768704409038640, 2430033853722917040

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn
• frac

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195551, A195552.

Programs

Mathematica

r = 3/2; z = 21;
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}]]  (* A195550, A195551 *)
Sqrt[a^2 + b^2] (* A195552 *)
(* Peter J. C. Moses, Sep 02 2011 *)