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A195541 Denominators a(n) of Pythagorean approximations b(n)/a(n) to e. 4
5, 12, 44, 51, 280, 949, 103488, 133416, 4142957, 81015132, 141119360, 2339121011, 22104171804, 658972588452, 461228244281, 3140753982224, 7467448353120, 49702513350325, 3912991025369532, 130254818350668557, 177768662787348689760 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Table of n, a(n) for n=1..21.

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 *)

CROSSREFS

Cf. A195500, A195542, A195543.

Sequence in context: A187916 A052644 A052280 * A006078 A046612 A254217

Adjacent sequences:  A195538 A195539 A195540 * A195542 A195543 A195544

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved

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Last modified December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)