

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
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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



