A195574 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2/5.

1, 12, 651, 5720, 12480, 17549, 236588, 12758199, 112130200, 244626200, 343998201, 4637596612, 250086218851, 2197976167920, 4795162766680, 6743052715749, 90906168553188, 4902190049156399, 43084728731444400, 93994780307828400

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195575, A195576.

Programs

Mathematica

r = 2/5; 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}]]  (* A195574, A195575 *)
Sqrt[a^2 + b^2] (* A195576 *)
(* Peter J. C. Moses, Sep 02 2011 *)