A195580 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 4/5.

4, 600, 2600, 15996, 2460800, 10652800, 65552004, 10084355800, 43655173800, 268632095996, 41325687609600, 178898891577600, 1100854263840004, 169352657739783000, 733127614029833000, 4511300504584239996, 694007150091943126400

Offset: 1

Author

Clark Kimberling, Sep 21 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195611, A195612.

Programs

Mathematica

r = 4/5; z = 18;
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}]]  (* A195580, A195611 *)
Sqrt[a^2 + b^2] (* A195612 *)
(* Peter J. C. Moses, Sep 02 2011 *)