A195680 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(12).

7, 2772, 5945, 26144, 285621, 257076560, 2386970016, 103850955649, 254621037540, 3060691213613, 29733959304728, 62837775720000, 89511043811115, 453985767379732, 1567652657852541, 35830073055128140, 22926879590846577132

Offset: 1

Author

Clark Kimberling, Sep 22 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195681, A195682.

Programs

Mathematica

r = Sqrt[12]; z = 24;
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}]]  (* A195680, A195681 *)
Sqrt[a^2 + b^2] (* A195682 *)
(* Peter J. C. Moses, Sep 02 2011 *)