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

%I #11 Dec 07 2016 10:32:28

%S 8,5,84,2400,1691,11480,118455,352692,1401961,1663145124,1802526192,

%T 15798984680,297278169720,1479041362764,1551248530483,42254295673488,

%U 1445285680561323,28154300465964144,49087267967218280,373205366478956820

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(5).

%C See A195500 for a discussion and references.

%t r = Sqrt[5]; z = 24;

%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}]] (* A195532, A195533 *)

%t Sqrt[a^2 + b^2] (* A195534 *)

%t (* by _Peter J. C. Moses_, Sep 02 2011 *)

%Y Cf. A195500, A195533, A195534.

%K nonn,frac

%O 1,1

%A _Clark Kimberling_, Sep 20 2011