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 A355953 #12 Jun 18 2023 01:52:04 %S A355953 5,1,4,6,8,6,8,5,2,8,2,7,2,8,5,3,7,0,8,5,3,9,6,9,1,1,6,3,2,0,7,5,2,7, %T A355953 1,9,3,0,1,2,9,3,1,8,4,2,1,5,7,6,5,6,3,0,4,5,6,0,6,9,2,6,7,3,0,9,8,0, %U A355953 8,2,8,9,2,6,9,2,6,6,1,6,5,0,0,5,4 %N A355953 Decimal expansion of (gamma + log(8)/2)/Pi. %C A355953 This constant is the additive part A in the asymptotic behavior of the resistance R between two nodes in an infinite square lattice of one-ohm resistors separated by the distance vector (i,j): R(i,j) = log(sqrt(i^2+j^2))/Pi + A. From an engineering point of view, this constant summand can be regarded as a kind of near-field contribution, which contains the well-known resistance of 1/2 ohms between 2 neighboring nodes as the main part. %C A355953 See, e.g., Cserti (1999) formula (33) on page 5 and Appendix B, pages 15 and 16, for a derivation of the parts of the constant. %H A355953 József Cserti, <a href="https://doi.org/10.1119/1.1285881">Application of the lattice Green's function for calculating the resistance of an infinite network of resistors</a>, American Journal of Physics, Vol. 68, No. 10 (2000), pp. 896-906; <a href="https://arxiv.org/abs/cond-mat/9909120">arXiv preprint</a>, arXiv:cond-mat/9909120 [cond-mat.mes-hall], 1999-2000. %e A355953 0.5146868528272853708539691163207527193... %t A355953 RealDigits[(EulerGamma + Log[8]/2)/Pi, 10, 120][[1]] (* _Amiram Eldar_, Jun 18 2023 *) %o A355953 (PARI) (Euler + log(8)/2)/Pi %Y A355953 Cf. A001620, A016631, A355955, A355954 (similar for triangular lattice). %Y A355953 Cf. A355565, A355566, A355567 (exact solutions for small distances). %K A355953 nonn,cons %O A355953 0,1 %A A355953 _Hugo Pfoertner_, Jul 26 2022