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

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%I A195634 #11 Mar 11 2014 01:41:27
%S A195634 4,55,1120,2997,35460,3140676,1921787,32412552,58579212,441025780,
%T A195634 410535015,77779347592,654610870027,2025218645520,7961709199049,
%U A195634 29306172663680,88433963478036,109778426942667,2900499582545112,4716082204442140
%N A195634 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3/4).
%C A195634 See A195500 for a discussion and references.
%t A195634 r = Sqrt[3/4]; z = 28;
%t A195634 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195634       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195634          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195634      Array[FromContinuedFraction[
%t A195634         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195634 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195634   p[{r, z}]]  (* A195634, A195635 *)
%t A195634 Sqrt[a^2 + b^2] (* A195636 *)
%t A195634 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195634 Cf. A195500, A195635, A195636.
%K A195634 nonn
%O A195634 1,1
%A A195634 _Clark Kimberling_, Sep 22 2011