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A195631
Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(2/3).
4
4, 171, 3304, 36456, 193028, 198629, 64044140, 3209176272, 2089963197, 14714161192, 151173075361, 450458512764, 1490895165780, 4767682119956876, 19409457907183648, 293100434264580753, 818944253254104320, 19191303984466705047
OFFSET
1,1
COMMENTS
See A195500 for a discussion and references.
MATHEMATICA
r = Sqrt[2/3]; z = 28;
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}]] (* A195631, A195632 *)
Sqrt[a^2 + b^2] (* A195633 *)
(* Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 22 2011
STATUS
approved