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 A242208 #24 Feb 03 2025 09:59:04 %S A242208 6,9,4,2,4,1,9,1,3,6,3,0,6,1,7,3,0,1,7,3,8,7,9,0,2,6,6,8,9,8,5,9,5,2, %T A242208 2,3,4,6,3,5,6,7,2,8,5,2,2,7,1,2,9,7,1,5,9,8,0,9,8,9,8,6,6,5,4,1,4,0, %U A242208 5,7,4,4,1,0,5,0,1,1,7,6,1,8,9,7,6,3,1,4,1,7,2,3,4,7,6,4,5,3,5,9 %N A242208 Decimal expansion of log_2(phi), the logarithm to base 2 of phi, the "golden ratio" (1+sqrt(5))/2. %C A242208 The limiting fractal dimension of a pattern generated by cellular automaton rule 150 is 1+log_2(phi). %C A242208 This number is also involved in the evaluation of asymptotics for the number of odd terms in Pascal's trinomial triangle. %C A242208 Also, the solution to 1 + 2^x = 4^x. See A328900 for solution to 2^x + 3^x = 4^x. - _M. F. Hasler_, Oct 30 2019 %H A242208 Steven Finch, Pascal Sebah and Zai-Qiao Bai, <a href="https://arxiv.org/abs/0802.2654">Odd Entries in Pascal's Trinomial Triangle</a>, arXiv:0802.2654 [math.NT], 2008, page 5. %H A242208 Daniel Glasscock, Joel Moreira, and Florian K. Richter, <a href="https://arxiv.org/abs/2007.05480">Additive transversality of fractal sets in the reals and the integers</a>, arXiv:2007.05480 [math.NT], 2020. See p. 33. %H A242208 Stephen Wolfram, <a href="http://lattice.ifsc.usp.br/~lattice/oldlattice/artigo-wolfram-cellular-autom.pdf">Statistical mechanics of cellular automata</a>, page 616. %H A242208 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>. %F A242208 log((1 + sqrt(5))/2)/log(2). %F A242208 log(sqrt(5) + 1)/log(2) - 1. - _M. F. Hasler_, Oct 30 2019 %e A242208 0.6942419136306173017387902668985952234635672852271297159809898665414... %t A242208 RealDigits[Log[2, GoldenRatio], 10, 100] // First %o A242208 (PARI) print(c=log(sqrt(5)+1)/log(2)-1); digits(c\.1^default(realprecision))[^-1] \\ [^-1] to discard possibly incorrect last digit. Use e.g. \p999 to get more digits. - _M. F. Hasler_, Oct 30 2019 %Y A242208 Cf. A001622, A328912 (continued fraction). %K A242208 nonn,cons %O A242208 0,1 %A A242208 _Jean-François Alcover_, May 07 2014