A195577 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/5.

1, 4, 56, 299, 1020, 3180, 3901, 20944, 272996, 1465799, 4993800, 15577800, 19105801, 102585004, 1337133056, 7179484499, 24459629220, 76300063380, 93580208101, 502461329944, 6549277433996, 35165113611599, 119803258923600

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn
• frac

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195578, A195579.

Programs

Mathematica

r = 3/5; 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}]]  (* A195577, A195578 *)
Sqrt[a^2 + b^2] (* A195579 *)
(* Peter J. C. Moses, Sep 02 2011 *)

Extensions

Typos in crossrefs fixed by Colin Barker, Jun 04 2015