Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Mar 09 2014 13:41:14
%S 4,171,3304,36456,193028,198629,64044140,3209176272,2089963197,
%T 14714161192,151173075361,450458512764,1490895165780,4767682119956876,
%U 19409457907183648,293100434264580753,818944253254104320,19191303984466705047
%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).
%C See A195500 for a discussion and references.
%t r = Sqrt[2/3]; 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}]] (* A195631, A195632 *)
%t Sqrt[a^2 + b^2] (* A195633 *)
%t (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y Cf. A195500, A195632, A195633.
%K nonn
%O 1,1
%A _Clark Kimberling_, Sep 22 2011