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

Offset: 0

Author

Thomas Anton, Jun 21 2021

Keywords

• nonn
• cons
• easy

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

Examples

			0.57389678734815951850857451...
		

Links

• Thomas Anton, Table of n, a(n) for n = 0...259
• Index entries for transcendental numbers

Crossrefs

Cf. A000328, A103710, A103711, A103712.

Programs

Mathematica

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

PARI

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

Formula

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

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