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A195574 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2/5. 4

%I #11 Mar 11 2014 01:40:39

%S 1,12,651,5720,12480,17549,236588,12758199,112130200,244626200,

%T 343998201,4637596612,250086218851,2197976167920,4795162766680,

%U 6743052715749,90906168553188,4902190049156399,43084728731444400,93994780307828400

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

%C See A195500 for a discussion and references.

%t r = 2/5; z = 26;

%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}]] (* A195574, A195575 *)

%t Sqrt[a^2 + b^2] (* A195576 *)

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

%Y Cf. A195500, A195575, A195576.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 21 2011

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)