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A305326 Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 1. 3
2, 2, 1, 4, 3, 1, 9, 7, 4, 3, 3, 7, 7, 5, 3, 5, 1, 8, 7, 4, 1, 5, 4, 9, 7, 7, 0, 0, 8, 4, 8, 5, 8, 0, 4, 8, 8, 9, 0, 7, 9, 1, 9, 6, 3, 7, 2, 1, 9, 4, 9, 9, 4, 3, 4, 3, 3, 1, 3, 8, 2, 3, 1, 6, 5, 0, 9, 1, 2, 8, 0, 4, 6, 4, 3, 3, 2, 6, 6, 2, 7, 4, 7, 9, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, the greatest root of x^3 - 4*x - 2;

Middle root: A305327;

Least root:  A305328.

LINKS

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

FORMULA

greatest:  (4 cos[1/3 arctan[sqrt[37/3]/3]])/sqrt[3]

middle:

-((2 cos[1/3 arctan[sqrt[37/3]/3]])/sqrt[3]) + 2 sin[1/3 arctan[sqrt[37/3]/3]]

least:

-((2 cos[1/3 arctan[sqrt[37/3]/3]])/sqrt[3]) - 2 sin[1/3 arctan[sqrt[37/3]/3]]

EXAMPLE

greatest root: 2.214319743377535187...

middle root: -0.539188872810889116...

least root: -1.67513087056664607088...

MATHEMATICA

r[x_] := 1/x + 1/(x + 1) + 1/(x + 2);

-Numerator[Factor[r[x] - 1]]

t = x /. ComplexExpand[Solve[r[x] == 1, x]]

u = N[t, 120]

RealDigits[u[[1]]]  (* A305326 *)

RealDigits[u[[2]]]  (* A305327 *)

RealDigits[u[[3]]]  (* A305328 *)

CROSSREFS

Cf. A305327, A305328.

Sequence in context: A197376 A113072 A328025 * A122918 A177424 A286332

Adjacent sequences:  A305323 A305324 A305325 * A305327 A305328 A305329

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, May 30 2018

STATUS

approved

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Last modified December 4 11:28 EST 2021. Contains 349486 sequences. (Running on oeis4.)