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A195580 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 4/5.

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%I A195580 #11 Mar 11 2014 01:40:52
%S A195580 4,600,2600,15996,2460800,10652800,65552004,10084355800,43655173800,
%T A195580 268632095996,41325687609600,178898891577600,1100854263840004,
%U A195580 169352657739783000,733127614029833000,4511300504584239996,694007150091943126400
%N A195580 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 4/5.
%C A195580 See A195500 for a discussion and references.
%t A195580 r = 4/5; z = 18;
%t A195580 p[{f_, n_}] := (#1[[2]]/#1[[
%t A195580       1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
%t A195580          2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
%t A195580      Array[FromContinuedFraction[
%t A195580         ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
%t A195580 {a, b} = ({Denominator[#1], Numerator[#1]} &)[
%t A195580   p[{r, z}]]  (* A195580, A195611 *)
%t A195580 Sqrt[a^2 + b^2] (* A195612 *)
%t A195580 (* _Peter J. C. Moses_, Sep 02 2011 *)
%Y A195580 Cf. A195500, A195611, A195612.
%K A195580 nonn
%O A195580 1,1
%A A195580 _Clark Kimberling_, Sep 21 2011