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%I #13 Dec 07 2016 10:29:18
%S 1,4,756,435,7480,1760400,178342500,107770201,77071637784,85438755160,
%T 162402622743,150321171634588,314779738565193,1395140327976600,
%U 3899078438579384,26320772661145332,506075333191877232,6916169937061302541
%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(1/2).
%C See A195500 for a discussion and references.
%t r = Sqrt[1/2]; z = 30;
%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}]] (* A195625, A195626 *)
%t Sqrt[a^2 + b^2] (* A195627 *)
%t (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y Cf. A195500, A195626, A195627.
%K nonn,frac
%O 1,2
%A _Clark Kimberling_, Sep 22 2011
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