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 A114431 #19 Apr 15 2020 11:39:04 %S A114431 2,4,6,7,5,0,3,8,5,7,0,5,6,5,1,7,5,7,6,3,8,1,8,8,6,7,5,5,3,5,8,7,8,6, %T A114431 0,7,0,3,8,2,2,5,4,4,7,5,0,6,2,3,7,2,9,8,8,4,6,4,0,1,9,7,7,4,0,5,5,0, %U A114431 7,5,1,9,3,5,9,1,7,7,3,3,9,7,1,5,8,1,5,9,5,1,6,3,4,9,2,3,8,6,3,5,7,5,3,9,3 %N A114431 Decimal expansion of the real solution of x^3 - x^2 - 2x - 4 = 0. %C A114431 The solution of the equation is twice the value of an upper bound on randomly generated Fibonacci-like sequences. %C A114431 Also, 1/log_2(x), where x is this constant, is the exponent in the exponent of the growth rate of the first Grigorchuk group. - _Andrey Zabolotskiy_, Apr 14 2020 %H A114431 Anna Erschler & Tianyi Zheng, <a href="https://doi.org/10.1007/s00222-019-00922-0">Growth of periodic Grigorchuk groups</a>, Invent. math. 219, 1069-1155 (2020). %H A114431 Eran Makover and Jeffrey McGowan, <a href="http://dx.doi.org/10.1016/j.jnt.2006.01.002">An elementary proof that random Fibonacci sequences grow exponentially</a>, Journal of Number Theory, Volume 121, Issue 1, November 2006, Pages 40-44. (arXiv:math/0510159 [math.NT]) %H A114431 Wikipedia, <a href="https://en.wikipedia.org/wiki/Grigorchuk_group">Grigorchuk group</a> %t A114431 RealDigits[x/.FindRoot[x^3 - x^2 - 2x == 4, {x, 2}, WorkingPrecision -> 120], 10, 120] [[1]] (* or *) RealDigits[(1 + Surd[64 - 3 * Sqrt[417], 3] + Surd[64 + 3 * Sqrt[417], 3])/3, 10, 120][[1]] (* _Harvey P. Dale_, Dec 02 2017 *) %o A114431 (PARI) default(realprecision, 105); 1/3*(1+(64-3*sqrt(417))^(1/3)+(64+3*sqrt(417))^(1/3)) \\ _Michel Marcus_, Jun 14 2013 %Y A114431 Cf. A114427. %K A114431 cons,nonn %O A114431 0,1 %A A114431 _Stefan Steinerberger_, Feb 13 2006