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A195532
Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(5).
4
8, 5, 84, 2400, 1691, 11480, 118455, 352692, 1401961, 1663145124, 1802526192, 15798984680, 297278169720, 1479041362764, 1551248530483, 42254295673488, 1445285680561323, 28154300465964144, 49087267967218280, 373205366478956820
OFFSET
1,1
COMMENTS
See A195500 for a discussion and references.
MATHEMATICA
r = Sqrt[5]; z = 24;
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}]] (* A195532, A195533 *)
Sqrt[a^2 + b^2] (* A195534 *)
(* by Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Sep 20 2011
STATUS
approved