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A195631 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3). 4

%I #8 Mar 09 2014 13:41:14

%S 4,171,3304,36456,193028,198629,64044140,3209176272,2089963197,

%T 14714161192,151173075361,450458512764,1490895165780,4767682119956876,

%U 19409457907183648,293100434264580753,818944253254104320,19191303984466705047

%N Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).

%C See A195500 for a discussion and references.

%t r = Sqrt[2/3]; z = 28;

%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}]] (* A195631, A195632 *)

%t Sqrt[a^2 + b^2] (* A195633 *)

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

%Y Cf. A195500, A195632, A195633.

%K nonn

%O 1,1

%A _Clark Kimberling_, Sep 22 2011

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Last modified April 30 12:47 EDT 2024. Contains 372134 sequences. (Running on oeis4.)