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A195565 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/4. 4
4, 3, 204, 280, 2280, 12596, 12797, 831996, 1149440, 9341440, 51622404, 52441603, 3409523404, 4710402840, 38281220840, 211548594996, 214905676797, 13972226073596, 19303229690880, 156876433658880, 866926090675204, 880683411072003 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A195500 for a discussion and references.
LINKS
MATHEMATICA
r = 5/4; 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}]] (* A195565, A195566 *)
Sqrt[a^2 + b^2] (* A195567 *)
(* by Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
Sequence in context: A325871 A079324 A002298 * A368301 A356855 A335913
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 21 2011
STATUS
approved

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Last modified June 22 03:16 EDT 2024. Contains 373561 sequences. (Running on oeis4.)