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A195553 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/2.

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%I A195553 #12 Dec 07 2016 10:34:49
%S A195553 5,260,7020,94635,5103280,137599280,1855038645,100034487540,
%T A195553 2697221086300,36362467421275,1960876019662560,52870927596046560,
%U A195553 712777084536797285,38437091637391006820,1036375920040483589580,13971856374727832955915
%N A195553 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/2.
%C A195553 See A195500 for a discussion and references.
%t A195553 r = 5/2; z = 18;
%t A195553 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195553       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195553          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195553      Array[FromContinuedFraction[
%t A195553         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195553 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195553   p[{r, z}]]  (* A195553, A195554 *)
%t A195553 Sqrt[a^2 + b^2] (* A195555 *)
%t A195553 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195553 Cf. A195500, A195554, A195555.
%K A195553 nonn,frac
%O A195553 1,1
%A A195553 _Clark Kimberling_, Sep 21 2011