A195634 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3/4).

4, 55, 1120, 2997, 35460, 3140676, 1921787, 32412552, 58579212, 441025780, 410535015, 77779347592, 654610870027, 2025218645520, 7961709199049, 29306172663680, 88433963478036, 109778426942667, 2900499582545112, 4716082204442140

Offset: 1

Author

Clark Kimberling, Sep 22 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195635, A195636.

Programs

Mathematica

r = Sqrt[3/4]; 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}]]  (* A195634, A195635 *)
Sqrt[a^2 + b^2] (* A195636 *)
(* Peter J. C. Moses, Sep 02 2011 *)