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 A316256 Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 3. 4
 1, 6, 8, 3, 7, 6, 1, 8, 3, 6, 6, 7, 8, 0, 3, 4, 3, 1, 2, 9, 0, 6, 6, 5, 2, 5, 9, 4, 2, 5, 1, 7, 0, 2, 6, 1, 6, 4, 7, 6, 3, 3, 7, 0, 8, 9, 7, 9, 4, 2, 7, 6, 1, 5, 3, 6, 1, 4, 9, 2, 7, 3, 0, 0, 2, 9, 0, 8, 2, 1, 5, 3, 6, 3, 3, 6, 9, 2, 6, 8, 6, 1, 0, 2, 3, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, the least root of 3*x^3 + 15*x^2 + 12 x - 8. Least: A316255; Greatest: A316257. See A305328 for a guide to related sequences. LINKS FORMULA greatest root: -(5/3) + (2/3) sqrt(13) cos((1/3) arctan(6 sqrt(61))) **** middle: -(5/3) - (1/3) sqrt(13) cos((1/3) arctan(6 sqrt(61))) - sqrt(13/3) sin((1/3) arctan(6 sqrt(61))) **** least: -(5/3) - (1/3) sqrt(13) cos((1/3) arctan(6 sqrt(61))) + sqrt(13/3) sin((1/3) arctan(6 sqrt(61))) EXAMPLE greatest root: 0.4234942709347976489... middle root: -1.683761836678034312... least root: -3.739732434256763336... MATHEMATICA a = 1; b = 1; c = 1; u = 0; v = 2; w = 4; d = 3; r[x_] := a/(x + u) + b/(x + v) + c/(x + w); t = x /. ComplexExpand[Solve[r[x] == d, x]] N[t, 20] y = Re[N[t, 200]]; RealDigits[y[[1]]] (* A316257, greatest *) RealDigits[y[[2]]] (* A316255, least *) RealDigits[y[[3]]] (* A316256, middle *) CROSSREFS Cf. A305328, A316255, A316257. Sequence in context: A196768 A021598 A021940 * A054042 A184084 A255728 Adjacent sequences:  A316253 A316254 A316255 * A316257 A316258 A316259 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 14 2018 STATUS approved

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Last modified October 21 21:46 EDT 2019. Contains 328315 sequences. (Running on oeis4.)