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A195687 Denominators a(n) of Pythagorean approximations b(n)/a(n) to (1+sqrt(5))/2 (the golden ratio).

%I A195687 #9 Mar 09 2014 13:41:25
%S A195687 3,8,28,1863,4400,433008,262353,352207108,379920428,18418959496,
%T A195687 91011249895,978117768540,11516765628956,1219780690817560,
%U A195687 708294344602810604,25852535312829023356,229222230912132985022679
%N A195687 Denominators a(n) of Pythagorean approximations b(n)/a(n) to (1+sqrt(5))/2 (the golden ratio).
%C A195687 See A195500 for a discussion and references.
%t A195687 r = GoldenRatio; z = 24;
%t A195687 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195687       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195687          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195687      Array[FromContinuedFraction[
%t A195687         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195687 {a, b} = ({Denominator[#1], Numerator[#1]} &)[p[{r, z}]]  (* A195687, A195688 *)
%t A195687 Sqrt[a^2 + b^2] (* A195689 *)
%t A195687 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195687 Cf. A195500, A195681, A195682.
%K A195687 nonn
%O A195687 1,1
%A A195687 _Clark Kimberling_, Sep 22 2011