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 A195550 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2. 4

%I

%S 3,60,660,3597,78480,856080,4669203,101866380,1111191780,6060621597,

%T 132222483360,1442326073760,7866682164003,171624681534300,

%U 1872138132549300,10210947388253997,222768704409038640,2430033853722917040

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2.

%C See A195500 for a discussion and references.

%t r = 3/2; 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}]] (* A195550, A195551 *)

%t Sqrt[a^2 + b^2] (* A195552 *)

%t (* by Peter Moses, Sep 2 2011 *)

%Y Cf. A195500, A195551, A195552.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 21 2011

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Last modified May 24 07:09 EDT 2013. Contains 225617 sequences.