OFFSET
0,1
COMMENTS
The limiting fractal dimension of a pattern generated by cellular automaton rule 150 is 1+log_2(phi).
This number is also involved in the evaluation of asymptotics for the number of odd terms in Pascal's trinomial triangle.
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
LINKS
Steven Finch, Pascal Sebah and Zai-Qiao Bai, Odd Entries in Pascal's Trinomial Triangle, arXiv:0802.2654 [math.NT], 2008, page 5.
Daniel Glasscock, Joel Moreira, and Florian K. Richter, Additive transversality of fractal sets in the reals and the integers, arXiv:2007.05480 [math.NT], 2020. See p. 33.
Stephen Wolfram, Statistical mechanics of cellular automata, page 616.
FORMULA
log((1 + sqrt(5))/2)/log(2).
log(sqrt(5) + 1)/log(2) - 1. - M. F. Hasler, Oct 30 2019
EXAMPLE
0.6942419136306173017387902668985952234635672852271297159809898665414...
MATHEMATICA
RealDigits[Log[2, GoldenRatio], 10, 100] // First
PROG
(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
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, May 07 2014
STATUS
approved