A195541 Denominators a(n) of Pythagorean approximations b(n)/a(n) to e.

5, 12, 44, 51, 280, 949, 103488, 133416, 4142957, 81015132, 141119360, 2339121011, 22104171804, 658972588452, 461228244281, 3140753982224, 7467448353120, 49702513350325, 3912991025369532, 130254818350668557, 177768662787348689760

Offset: 1

Author

Clark Kimberling, Sep 20 2011

Keywords

• nonn

Comments

See A195500 for a discussion and references.

Crossrefs

Cf. A195500, A195542, A195543.

Programs

Mathematica

r = E; z = 23;
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}]]  (* A195541, A195542 *)
Sqrt[a^2 + b^2] (* A195543 *)
(* Peter J. C. Moses, Sep 02 2011 *)