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A195574
Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2/5.
4
1, 12, 651, 5720, 12480, 17549, 236588, 12758199, 112130200, 244626200, 343998201, 4637596612, 250086218851, 2197976167920, 4795162766680, 6743052715749, 90906168553188, 4902190049156399, 43084728731444400, 93994780307828400
OFFSET
1,2
COMMENTS
See A195500 for a discussion and references.
MATHEMATICA
r = 2/5; z = 26;
p[{f_, n_}] := (#1[[2]]/#1[[
1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[
2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[
Array[FromContinuedFraction[
ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];
{a, b} = ({Denominator[#1], Numerator[#1]} &)[
p[{r, z}]] (* A195574, A195575 *)
Sqrt[a^2 + b^2] (* A195576 *)
(* Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 21 2011
STATUS
approved