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A316252
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Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
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4
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2, 7, 8, 4, 2, 1, 8, 6, 9, 1, 4, 5, 7, 7, 1, 0, 3, 6, 2, 9, 3, 4, 7, 1, 2, 0, 7, 9, 4, 9, 9, 5, 2, 7, 6, 9, 9, 7, 2, 1, 3, 3, 0, 0, 6, 8, 6, 0, 9, 4, 7, 7, 6, 7, 5, 2, 0, 9, 6, 7, 9, 6, 7, 8, 0, 8, 9, 4, 7, 0, 4, 6, 2, 8, 4, 7, 5, 0, 2, 0, 0, 0, 9, 4, 2, 3
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OFFSET
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1,1
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COMMENTS
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Equivalently, the least root of 3*x^3 + 12*x^2 + 8 x - 6;
See A305328 for a guide to related sequences.
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LINKS
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FORMULA
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greatest root: -(4/3) + (4/3) sqrt(2) cos((1/3) arctan(sqrt(391)/11))
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middle: -(4/3) - (2/3) sqrt(2) cos((1/3) arctan(sqrt(391)/11)) + 2 sqrt(2/3) sin((1/3) arctan(sqrt(391)/11))
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least: -(4/3) - (2/3) sqrt(2) cos((1/3) arctan(sqrt(391)/11)) - 2 sqrt(2/3) sin((1/3) arctan(sqrt(391)/11))
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EXAMPLE
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greatest root: 0.4351172195495135109...
middle root: -1.650898528091803148...
least root: -2.784218691457710362...
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MATHEMATICA
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a = 1; b = 1; c = 1; u = 0; v = 2; w = 3; 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]]] (* A316254, greatest *)
RealDigits[y[[2]]] (* A316252, least *)
RealDigits[y[[3]]] (* A316253, middle *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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