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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
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
Sequence in context: A339029 A297757 A223249 * A248135 A307916 A280660
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Sep 20 2011
STATUS
approved

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Last modified July 20 20:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)