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 A195559 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2/3. 4
 1, 4, 91, 240, 840, 989, 5396, 117719, 312120, 1089720, 1284121, 7003804, 152799571, 405130920, 1414456320, 1666787669, 9090932396, 198333725039, 525859622640, 1835963213040, 2163489110641, 11800023246004, 257437022301451 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A195500 for a discussion and references. LINKS MATHEMATICA r = 2/3; z = 25; 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}]] (* A195559, A195560 *) Sqrt[a^2 + b^2] (* A195561 *) (* Peter J. C. Moses, Sep 02 2011 *) CROSSREFS Cf. A195500, A195560, A195561. Sequence in context: A146506 A202575 A201721 * A195551 A024261 A337827 Adjacent sequences: A195556 A195557 A195558 * A195560 A195561 A195562 KEYWORD nonn AUTHOR Clark Kimberling, Sep 21 2011 STATUS approved

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Last modified February 6 23:12 EST 2023. Contains 360111 sequences. (Running on oeis4.)