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 A316259 Decimal expansion of the middle x such that 1/x + 1/(x+3) + 1/(x+4) = 3 (negated). 4
 2, 6, 2, 3, 3, 2, 4, 9, 0, 1, 9, 9, 8, 1, 3, 1, 6, 3, 4, 2, 9, 9, 6, 1, 3, 8, 1, 1, 8, 8, 9, 9, 9, 7, 4, 6, 8, 7, 2, 6, 5, 8, 2, 7, 8, 7, 6, 7, 5, 6, 1, 1, 5, 2, 9, 8, 3, 9, 9, 4, 0, 5, 0, 9, 8, 9, 1, 7, 7, 6, 6, 4, 1, 9, 0, 0, 4, 0, 9, 2, 4, 0, 7, 7, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, the least root of 3*x^3 + 18*x^2 + 22 x - 12. Least:: A316258 Greatest: A316260; See A305328 for a guide to related sequences. LINKS Muniru A Asiru, Table of n, a(n) for n = 1..1000 FORMULA greatest root: -2 + (2/3) sqrt(14) cos((1/3) arctan(sqrt(181/2)/9)) **** middle: -2 - (1/3)sqrt(14) cos((1/3) arctan(sqrt(181/2)/9)) + sqrt(14/3) sin((1/3) arctan(sqrt(181/2)/9)) **** least: -2 - 1/3 sqrt(14) cos((1/3) arctan(sqrt(181/2)/9)) - sqrt(14/3) sin((1/3) arctan(sqrt(181/2)/9)) EXAMPLE greatest root: 0.4033761543003640184... middle root: -2.623324901998131634... [Corrected by A.H.M. Smeets, Sep 17 2018] least root: -3.780051252302232384... MATHEMATICA a = 1; b = 1; c = 1; u = 0; v = 3; 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]]]  (* A316259, middle *) RealDigits[y[[2]]]  (* A316258, least *) RealDigits[y[[3]]]  (* A316260, greatest *) CROSSREFS Cf. A305328, A316258, A316260. Sequence in context: A330541 A320575 A110218 * A057892 A334188 A265993 Adjacent sequences:  A316256 A316257 A316258 * A316260 A316261 A316262 KEYWORD nonn,cons AUTHOR Clark Kimberling, Sep 14 2018 EXTENSIONS Name corrected by A.H.M. Smeets, Sep 17 2018 STATUS approved

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)