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A195568 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 7/4. 4
3, 8, 120, 637, 2176, 30848, 164483, 561288, 7958776, 42435837, 144810240, 2053333248, 10948281603, 37360480520, 529752019320, 2824614217597, 9638859164032, 136673967651200, 728739519858563, 2486788303839624, 35261353901990392 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
See A195500 for a discussion and references.
LINKS
FORMULA
Empirical g.f.: x*(3*x^6+8*x^5+120*x^4-134*x^3+120*x^2+8*x+3) / (x^9-257*x^6-257*x^3+1). - Colin Barker, Jun 04 2015
MATHEMATICA
r = 7/4; 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}]] (* A195568, A195569 *)
Sqrt[a^2 + b^2] (* A195570 *)
(* Peter J. C. Moses, Sep 02 2011 *)
CROSSREFS
Sequence in context: A279164 A134803 A030063 * A051047 A192629 A245458
KEYWORD
nonn
AUTHOR
Clark Kimberling, Sep 21 2011
STATUS
approved

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Last modified June 13 07:36 EDT 2024. Contains 373366 sequences. (Running on oeis4.)