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 A195538 Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(8). 4
 5, 12, 145, 420, 4901, 14280, 166465, 485112, 5654885, 16479540, 192099601, 559819260, 6525731525, 19017375312, 221682772225, 646030941360, 7530688524101, 21946034630940, 255821727047185, 745519146510612, 8690408031080165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A195500 for a discussion and references. Conjecture: a(n) = 35*a(n-2) - 35*a(n-4) + a(n-6) with bisections A098602 and A076218. - R. J. Mathar, Sep 21 2011 LINKS Table of n, a(n) for n=1..21. MATHEMATICA r = Sqrt[8]; 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}]] (* A195538, A195539 *) Sqrt[a^2 + b^2] (* A195540 *) (* Peter J. C. Moses, Sep 02 2011 *) CROSSREFS Cf. A195500, A195539, A195540. Sequence in context: A096314 A332466 A323565 * A330218 A047658 A290804 Adjacent sequences: A195535 A195536 A195537 * A195539 A195540 A195541 KEYWORD nonn,frac AUTHOR Clark Kimberling, Sep 20 2011 STATUS approved

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Last modified August 13 09:11 EDT 2024. Contains 375130 sequences. (Running on oeis4.)