A355186 Decimal expansion of 2*log(sqrt(2)+1)/Pi.

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

Offset

0,1

Comments

The average distance between the center of a unit square to a point on its perimeter uniformly chosen by a random direction from the center.

If the point is uniformly chosen at random on the perimeter, then the average is (sqrt(2) + arcsinh(1))/4 (A345653).

Links

Table of n, a(n) for n=0..104.

Mark Dalthorp, Escape the Square, Mathematics Magazine, Vol. 87, No. 1 (2014), p. 68.

Formula

Equals arcsinh(1)/arcsin(1).

Equals A060294 * A091648 = A091648 / A019669.

Example

0.56109985233918012713571958893523969280887242462809...

Mathematica

RealDigits[2*ArcSinh[1]/Pi, 10, 100][[1]]

Crossrefs

Cf. A019669, A060294, A091648, A345653.

Sequence in context: A105580 A047774 A243108 * A287610 A298171 A046614

Adjacent sequences: A355183 A355184 A355185 * A355187 A355188 A355189

Keyword

nonn,cons

Author

Amiram Eldar, Jun 23 2022

Status

approved