A395597 - OEIS

A395597

Decimal expansion of the aspect ratio of a rectangle with the property that a straight line drawn through a uniformly random point on one of the two larger sides, with direction chosen uniformly at random, intersects each of the three other sides with an equal probability.

1, 2, 6, 3, 1, 2, 2, 2, 1, 3, 9, 6, 9, 2, 6, 2, 5, 4, 2, 0, 2, 6, 2, 4, 9, 0, 4, 0, 5, 2, 2, 5, 8, 0, 4, 5, 1, 8, 6, 0, 2, 9, 7, 5, 7, 3, 3, 2, 3, 8, 7, 7, 1, 5, 2, 4, 5, 8, 8, 1, 1, 3, 5, 1, 9, 0, 3, 1, 9, 0, 1, 5, 7, 1, 7, 3, 1, 2, 4, 5, 1, 2, 8, 2, 0, 6, 7, 2, 4, 4, 6, 8, 4, 7, 7, 5, 2, 6, 7, 5, 1, 5, 6, 3, 1

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OFFSET

1,2

COMMENTS

The unique real solution to the equation 2*arctan(x) - log(1 + x^2)/x = Pi/3.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

1.263122213969262542026249040522580451860297573323877...

MATHEMATICA

RealDigits[r /. FindRoot[2*ArcTan[r] - Log[1 + r^2]/r == Pi/3, {r, 1}, WorkingPrecision -> 120]][[1]]

PROG