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A316137 Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 1. 4
3, 4, 8, 9, 2, 8, 8, 5, 7, 1, 8, 1, 0, 0, 7, 8, 7, 6, 2, 7, 9, 2, 9, 3, 6, 5, 3, 0, 4, 5, 4, 8, 4, 9, 2, 4, 1, 1, 6, 8, 0, 6, 5, 8, 3, 9, 4, 8, 2, 9, 9, 3, 1, 1, 5, 5, 3, 6, 5, 6, 6, 4, 5, 5, 1, 7, 0, 6, 7, 4, 9, 3, 4, 1, 4, 2, 6, 1, 6, 4, 1, 9, 3, 4, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Equivalently, the least root of x^3 + 3*x^2 - 4*x - 8;
Middle root: A316138;
Greatest root: A316139.
See A305328 for a guide to related sequences.
LINKS
FORMULA
greatest root: -1 + 2 sqrt[7/3] cos[1/3 arctan[(2 sqrt[79/3])/3]]
middle: -1 - sqrt[7/3] cos[1/3 arctan[(2 sqrt[79/3])/3]] + sqrt[7] sin[1/3 arctan[(2 sqrt[79/3])/3]]
least: -1 - sqrt[7/3] cos[1/3 arctan[(2 sqrt[79/3])/3]] - sqrt[7] sin[1/3 arctan[(2 sqrt[79/3])/3]]
EXAMPLE
greatest root: 1.7784571182583887319...
middle root: -1.2891685464483099691...
least root: -3.4892885718100787628...
MATHEMATICA
a = 1; b = 1; c = 1; u = 0; v = 2; w = 4; 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]]] (* A316137, least *)
RealDigits[u[[2]]] (* A316138, middle *)
RealDigits[u[[3]]] (* A316139, greatest *)
CROSSREFS
Sequence in context: A245026 A125219 A075562 * A089290 A296497 A019811
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 21 2018
STATUS
approved

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Last modified February 29 23:09 EST 2024. Contains 370428 sequences. (Running on oeis4.)