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 A195544 Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi. 4

%I

%S 12,52,315,1044,3296,20919,217620,450296,125510644,138980066871,

%T 289898680472,3593636117787,34812833117460,1934468176818608,

%U 1244148342635075,86081645453428848,8659539839551787053788,138771143651019468539176

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to Pi.

%C See A195500 for a discussion and references.

%t r = Pi; z = 21;

%t p[{f_, n_}] := (#1[[2]]/#1[[

%t 1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

%t 2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

%t Array[FromContinuedFraction[

%t ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

%t {a, b} = ({Denominator[#1], Numerator[#1]} &)[

%t p[{r, z}]] (* A195544, A195545 *)

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

%t (* _Peter J. C. Moses_, Sep 02 2011 *)

%Y Cf. A195500, A195545, A195546.

%K nonn,frac

%O 1,1

%A _Clark Kimberling_, Sep 20 2011

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Last modified November 30 16:13 EST 2021. Contains 349422 sequences. (Running on oeis4.)