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Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(6).
4

%I #12 Dec 07 2016 10:33:04

%S 5,1020,2247,2633277900,2640162496,638843546289,1396487515808,

%T 6103353023795,21860678072520,82495605773137,29466852345019792,

%U 34041728665663572,292320946605948260,262936589866701605,3964118460886936896

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(6).

%C See A195500 for a discussion and references.

%t r = Sqrt[6]; z = 18;

%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}]] (* A195535, A195536 *)

%t Sqrt[a^2 + b^2] (* A195537 *)

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

%Y Cf. A195500, A195536, A195537.

%K nonn,frac

%O 1,1

%A _Clark Kimberling_, Sep 20 2011