A345653 - OEIS

A345653

Decimal expansion of (sqrt(2) + arcsinh(1))/4.

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

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OFFSET

0,1

COMMENTS

Maximal value of the average distance from the set of lattice points of any line in the plane, where average distance is the limit of the integral of the distance to the set over a segment of the line centered around a fixed point, divided by the length of the segment, as that length approaches infinity, achieved precisely by lines x = z + 1/2 and y = z + 1/2 for integers z.

The average distance between the center of a unit square to a randomly and uniformly chosen point on its perimeter. - Amiram Eldar, Jun 23 2022

LINKS

Thomas Anton, Table of n, a(n) for n = 0...259

FORMULA

Equals Integral_{x=0..1/2} 2*sqrt(x^2+1/4) dx.

Equals (1/2) * A103711. - Amiram Eldar, Jun 23 2022

EXAMPLE

0.57389678734815951850857451...

MATHEMATICA

First[RealDigits[N[(Sqrt[2]+ArcSinh[1])/4, 100]]] (* Stefano Spezia, Jun 21 2021 *)

PROG

(PARI) (sqrt(2) + asinh(1))/4 \\ Michel Marcus, Jun 24 2021