This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345653 #24 Nov 21 2024 08:05:48
%S A345653 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,
%T A345653 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,
%U A345653 7,4,1,5,6,7,1,0,3,3,2,8,1,6,7,1,0,2,3
%N A345653 Decimal expansion of (sqrt(2) + arcsinh(1))/4.
%C A345653 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.
%C A345653 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
%H A345653 Thomas Anton, <a href="/A345653/b345653.txt">Table of n, a(n) for n = 0...259</a>
%H A345653 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A345653 Equals Integral_{x=0..1/2} 2*sqrt(x^2+1/4) dx.
%F A345653 Equals (1/2) * A103711. - _Amiram Eldar_, Jun 23 2022
%e A345653 0.57389678734815951850857451...
%t A345653 First[RealDigits[N[(Sqrt[2]+ArcSinh[1])/4,100]]] (* _Stefano Spezia_, Jun 21 2021 *)
%o A345653 (PARI) (sqrt(2) + asinh(1))/4 \\ _Michel Marcus_, Jun 24 2021
%Y A345653 Cf. A000328, A103710, A103711, A103712.
%K A345653 nonn,cons,easy
%O A345653 0,1
%A A345653 _Thomas Anton_, Jun 21 2021