A195625 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(1/2).

1, 4, 756, 435, 7480, 1760400, 178342500, 107770201, 77071637784, 85438755160, 162402622743, 150321171634588, 314779738565193, 1395140327976600, 3899078438579384, 26320772661145332, 506075333191877232, 6916169937061302541

Offset: 1

Author

Clark Kimberling, Sep 22 2011

Keywords

• nonn
• frac

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195626, A195627.

Programs

Mathematica

r = Sqrt[1/2]; z = 30;
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}]]  (* A195625, A195626 *)
Sqrt[a^2 + b^2] (* A195627 *)
(* Peter J. C. Moses, Sep 02 2011 *)