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A195680 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(12).

%I A195680 #12 Mar 11 2014 01:41:37
%S A195680 7,2772,5945,26144,285621,257076560,2386970016,103850955649,
%T A195680 254621037540,3060691213613,29733959304728,62837775720000,
%U A195680 89511043811115,453985767379732,1567652657852541,35830073055128140,22926879590846577132
%N A195680 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(12).
%C A195680 See A195500 for a discussion and references.
%t A195680 r = Sqrt[12]; z = 24;
%t A195680 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195680       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195680          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195680      Array[FromContinuedFraction[
%t A195680         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195680 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195680   p[{r, z}]]  (* A195680, A195681 *)
%t A195680 Sqrt[a^2 + b^2] (* A195682 *)
%t A195680 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195680 Cf. A195500, A195681, A195682.
%K A195680 nonn
%O A195680 1,1
%A A195680 _Clark Kimberling_, Sep 22 2011