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A195631 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).

%I A195631 #8 Mar 09 2014 13:41:14
%S A195631 4,171,3304,36456,193028,198629,64044140,3209176272,2089963197,
%T A195631 14714161192,151173075361,450458512764,1490895165780,4767682119956876,
%U A195631 19409457907183648,293100434264580753,818944253254104320,19191303984466705047
%N A195631 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).
%C A195631 See A195500 for a discussion and references.
%t A195631 r = Sqrt[2/3]; z = 28;
%t A195631 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195631       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195631          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195631      Array[FromContinuedFraction[
%t A195631         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195631 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195631   p[{r, z}]]  (* A195631, A195632 *)
%t A195631 Sqrt[a^2 + b^2] (* A195633 *)
%t A195631 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195631 Cf. A195500, A195632, A195633.
%K A195631 nonn
%O A195631 1,1
%A A195631 _Clark Kimberling_, Sep 22 2011