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

1,2

Comments

See A195500 for a discussion and references.

Links

Table of n, a(n) for n=1..18.

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 *)

Crossrefs

Cf. A195500, A195626, A195627.

Sequence in context: A160737 A128846 A332174 * A268838 A292306 A319943

Adjacent sequences: A195622 A195623 A195624 * A195626 A195627 A195628

Keyword

nonn,frac

Author

Clark Kimberling, Sep 22 2011

Status

approved