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A316255 Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 3. 4
3, 7, 3, 9, 7, 3, 2, 4, 3, 4, 2, 5, 6, 7, 6, 3, 3, 3, 6, 0, 7, 3, 7, 0, 8, 4, 2, 3, 3, 3, 9, 6, 8, 3, 1, 4, 3, 4, 1, 6, 4, 4, 4, 3, 7, 0, 1, 5, 4, 3, 0, 8, 9, 8, 3, 9, 3, 1, 5, 6, 8, 5, 9, 6, 7, 0, 9, 2, 4, 5, 2, 2, 8, 2, 5, 6, 1, 9, 0, 0, 8, 3, 2, 8, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, the least root of 3*x^3 + 15*x^2 + 12 x - 8.

Middle: A316256;

Greatest: A316257.

See A305328 for a guide to related sequences.

LINKS

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

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, A316256, A316257.

Sequence in context: A074176 A005596 A159566 * A096385 A205723 A088837

Adjacent sequences:  A316252 A316253 A316254 * A316256 A316257 A316258

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 14 2018

STATUS

approved

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Last modified December 11 07:46 EST 2019. Contains 329914 sequences. (Running on oeis4.)