A396271 - OEIS

A396271

Decimal expansion of the aspect ratio of a rectangle with the property that a straight line drawn through a uniformly random point on its perimeter, with direction chosen uniformly at random, intersects each of the opposite side to the side on which the point lies with probability 1/2.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The larger of the two real solutions of the equation (2*x*arctan(x) + 2*arccot(x) - x*log(x) - (x+1)*log(x^2+1))/(x+1) = Pi/2. The other solution is the reciprocal of this constant, 0.260792478389... .

LINKS

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

EXAMPLE

3.834466416270888353203856464620079966061356889592406...

MATHEMATICA

RealDigits[r /. FindRoot[(2*r*ArcTan[r] + 2*ArcCot[r] + 2*r*Log[r] - (r+1)*Log[r^2+1])/(r+1) == Pi/2, {r, 4}, WorkingPrecision -> 120]][[1]]

PROG

(PARI) solve(r = 3, 4, (2*r*atan(r) + 2*atan(1/r) + 2*r*log(r) - (r+1)*log(r^2+1))/(r+1) - Pi/2)

CROSSREFS

Cf. A156649, A284983, A300284, A395597, A395598, A396270.

Sequence in context: A198489 A334503 A015136 * A179450 A333287 A360199

Adjacent sequences: A396264 A396268 A396270 * A396272 A396273 A396274

KEYWORD

nonn,cons,new

AUTHOR

Amiram Eldar, May 21 2026

STATUS

approved