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A195544 Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi. 4
12, 52, 315, 1044, 3296, 20919, 217620, 450296, 125510644, 138980066871, 289898680472, 3593636117787, 34812833117460, 1934468176818608, 1244148342635075, 86081645453428848, 8659539839551787053788, 138771143651019468539176 (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..18.

MATHEMATICA

r = Pi; z = 21;

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}]]  (* A195544, A195545 *)

Sqrt[a^2 + b^2] (* A195546 *)

(* Peter J. C. Moses, Sep 02 2011 *)

CROSSREFS

Cf. A195500, A195545, A195546.

Sequence in context: A339029 A297757 A223249 * A248135 A307916 A280660

Adjacent sequences:  A195541 A195542 A195543 * A195545 A195546 A195547

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Sep 20 2011

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)