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 A316131 Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 1, negated. 4
 2, 5, 1, 4, 1, 3, 6, 9, 2, 9, 3, 3, 5, 2, 9, 1, 0, 7, 2, 6, 9, 3, 7, 7, 4, 8, 6, 6, 9, 6, 2, 2, 1, 7, 4, 7, 8, 0, 5, 2, 4, 7, 6, 3, 0, 0, 7, 4, 5, 4, 0, 4, 5, 9, 2, 2, 2, 1, 6, 7, 1, 3, 9, 4, 2, 0, 9, 3, 4, 1, 6, 5, 7, 2, 9, 1, 7, 7, 3, 5, 9, 0, 7, 5, 8, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, the least root of x^3 + x^2 - 5*x - 3; Middle root:  A316132; Greatest root:  A316133. See A305328 for a guide to related sequences. LINKS FORMULA greatest root:  -(1/3) + 8/3 Cos[1/3 ArcTan[(9 Sqrt[47])/17]] middle: -(1/3) - 4/3 Cos[1/3 ArcTan[(9 Sqrt[47])/17]] + (4 Sin[1/3 ArcTan[(9 Sqrt[47])/17]])/Sqrt[3] least: -(1/3) - 4/3 Cos[1/3 ArcTan[(9 Sqrt[47])/17]] - (4 Sin[1/3 ArcTan[(9 Sqrt[47])/17]])/Sqrt[3] EXAMPLE greatest root: 2.0861301976514940912... middle root: -0.57199326831620301856... least root: -2.5141369293352910727... MATHEMATICA a = 1; b = 1; c = 1; u = 0; v = 1; w = 3; d = 1; r[x_] := a/(x + u) + b/(x + v) + c/(x + w); t = x /. ComplexExpand[Solve[r[x] == d, x]] N[t, 20] u = N[t, 200]; RealDigits[u[[1]]]  (* A316131 *) RealDigits[u[[2]]]  (* A316132 *) RealDigits[u[[3]]]  (* A316133 *) PROG (PARI) solve(x=-3, -2, x^3+x^2-5*x-3) \\ Jianing Song, Aug 01 2018 CROSSREFS Cf. A305328, A316131, A316132. Sequence in context: A121428 A239969 A105686 * A153726 A229339 A274880 Adjacent sequences:  A316128 A316129 A316130 * A316132 A316133 A316134 KEYWORD nonn,cons AUTHOR Clark Kimberling, Jun 26 2018 STATUS approved

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Last modified July 24 04:08 EDT 2019. Contains 325290 sequences. (Running on oeis4.)