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A316246 Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 3. 4
1, 7, 9, 2, 5, 1, 7, 2, 1, 3, 9, 7, 4, 3, 4, 0, 2, 9, 1, 7, 3, 0, 1, 7, 3, 3, 1, 4, 9, 4, 1, 4, 1, 5, 5, 8, 5, 7, 5, 9, 8, 7, 3, 8, 2, 6, 2, 9, 1, 3, 2, 2, 0, 1, 9, 9, 0, 1, 2, 7, 7, 0, 6, 3, 9, 2, 5, 8, 4, 5, 3, 7, 8, 4, 1, 6, 1, 0, 5, 3, 4, 8, 6, 3, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Equivalently, the least root of 3*x^3 + 6*x^2 - 2;

Middle root: A316247;

Greatest root: A316248.

See A305328 for a guide to related sequences.

LINKS

Table of n, a(n) for n=1..86.

FORMULA

greatest root: -2/3 + (4/3)*cos((1/3)*arctan(3*sqrt(7)))

****

middle: -2/3 - (2/3)*cos((1/3)*arctan(3*sqrt(7))) + 2*sin((1/3)*arctan(3*sqrt(7)))/sqrt(3)

****

least: -2/3 - (2/3)*cos((1/3)*arctan(3*sqrt(7))) - 2*sin((1/3)*arctan(3*sqrt(7)))/sqrt(3)

EXAMPLE

greatest root: 0.5148689384387165869...

middle root: -0.7223517244643762951...

least root: -1.792517213974340291...

MATHEMATICA

a = 1; b = 1; c = 1; u = 0; v = 1; w = 2; d = 3;

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]]]  (* A316246, greatest *)

RealDigits[u[[2]]]  (* A316247, least *)

RealDigits[u[[3]]]  (* A316248, middle *)

CROSSREFS

Cf. A305328, A316247, A316248.

Sequence in context: A154197 A094148 A154215 * A249546 A110793 A199290

Adjacent sequences:  A316243 A316244 A316245 * A316247 A316248 A316249

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Aug 19 2018

EXTENSIONS

a(86) corrected by Andrew Howroyd, Nov 04 2018

STATUS

approved

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Last modified February 27 18:19 EST 2020. Contains 332307 sequences. (Running on oeis4.)