A195550 - OEIS

%I #10 Dec 07 2016 10:34:25

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

%Y Cf. A195500, A195551, A195552.

%K nonn,frac

%O 1,1

%A _Clark Kimberling_, Sep 21 2011