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A195634 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3/4). 4
4, 55, 1120, 2997, 35460, 3140676, 1921787, 32412552, 58579212, 441025780, 410535015, 77779347592, 654610870027, 2025218645520, 7961709199049, 29306172663680, 88433963478036, 109778426942667, 2900499582545112, 4716082204442140 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A195500 for a discussion and references.
LINKS
MATHEMATICA
r = Sqrt[3/4]; 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}]] (* A195634, A195635 *)
Sqrt[a^2 + b^2] (* A195636 *)
(* Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
Sequence in context: A202163 A073352 A258793 * A322627 A206384 A271715
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 22 2011
STATUS
approved

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)