A395598 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 the other larger side with probability 1/2.

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

Offset

1,1

Comments

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

Links

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

Example

2.445828316431492046186470886388920883276945104598903...

Mathematica

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

Prog

(PARI) solve(r = 2, 3, 2*atan(r) - log(1 + r^2)/r - Pi/2)

Crossrefs

Cf. A156649, A188582, A284983, A300284, A392572, A394923, A395597.

Sequence in context: A349462 A340761 A035625 * A219875 A132128 A280057

Adjacent sequences: A395594 A395596 A395597 * A395599 A395600 A395601

Keyword

nonn,cons

Author

Amiram Eldar, Apr 30 2026

Status

approved