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 A195634 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3/4). 4

%I

%S 4,55,1120,2997,35460,3140676,1921787,32412552,58579212,441025780,

%T 410535015,77779347592,654610870027,2025218645520,7961709199049,

%U 29306172663680,88433963478036,109778426942667,2900499582545112,4716082204442140

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3/4).

%C See A195500 for a discussion and references.

%t r = Sqrt[3/4]; z = 28;

%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}]] (* A195634, A195635 *)

%t Sqrt[a^2 + b^2] (* A195636 *)

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

%Y Cf. A195500, A195635, A195636.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 22 2011

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