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 A370088 #11 Feb 11 2024 09:16:50 %S A370088 3,5,6,6,6,6,8,3,6,7,1,2,8,8,9,5,8,2,8,3,7,3,0,7,3,8,1,0,0,1,2,6,6,2, %T A370088 6,9,9,0,3,8,7,0,1,5,3,4,0,7,6,2,4,4,1,3,9,9,0,6,0,9,7,3,7,6,3,7,3,6, %U A370088 1,3,8,4,2,0,8,8,8,5,5,4,8,5,1,9,6,7,2 %N A370088 Decimal expansion of the two-dimensional backbone constant. %C A370088 This constant is the negative of the exponent of the growth rate of the probability of Bernoulli percolation on the 2-dimensional triangular lattice at criticality (p = 1/2). It is transcendental (Theorem 1.2 in Nolin, Qian, Sun, & Zhuang). %H A370088 Pierre Nolin, Wei Qian, Xin Sun, and Zijie Zhuang, <a href="https://arxiv.org/abs/2309.05050">Backbone exponent for two-dimensional percolation</a>, arXiv preprint (2023). arXiv:2309.05050 [math.PR], 2023-2024. %H A370088 Leila Sloman, <a href="https://www.quantamagazine.org/maze-proof-establishes-a-backbone-for-statistical-mechanics-20240207/">Maze proof establishes a 'backbone' for statistical mechanics</a>, Quanta Magazine (2024). %H A370088 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A370088 This is the unique constant 1/4 < x < 2/3 with sqrt(36*x+3)/4 + sin(2*Pi*sqrt(12*x+1)/3) = 0. %e A370088 0.35666683671288958283730738100126626990387015340762441399060973763736138420.... %o A370088 (PARI) t=sqrt(3)/4; u=2*Pi/3; solve(x=.3,.4, my(s=sqrt(12*x+1)); sin(s*u)+s*t) %Y A370088 Cf. A003197, A003198, A003202, A006809. %K A370088 cons,nonn %O A370088 0,1 %A A370088 _Charles R Greathouse IV_, Feb 08 2024