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%I #22 Jul 16 2020 02:32:49
%S 7,9,2,4,8,1,2,5,0,3,6,0,5,7,8,0,9,0,7,2,6,8,6,9,4,7,1,9,7,3,9,0,8,2,
%T 5,4,3,7,9,9,0,7,2,0,3,8,4,6,2,4,0,5,3,0,2,2,7,8,7,6,3,2,7,2,7,0,5,4,
%U 9,1,1,3,8,9,7,1,7,9,2,8,1,2,6,1,1,4,0,2,3,7,4,5,9,0,4,4,1,2,1,0,4,5,4,9
%N Decimal expansion of log(3)/log(4).
%C Gelfond showed abs( sup{ x in R} sum(0<=n<N, (-1)^t(n)*exp(i*x*n) ) <=C*N^(log(3)/log(4)) where t(n) is the Thue-Morse sequence and the exponent log(3)/log(4) is optimal.
%D J.-P. Allouche & J. Shallit, Automatic sequences, Cambridge University Press, 2003, p 122
%H Vincenzo Librandi, <a href="/A094148/b094148.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Integral_{x=1..oo} 1/(2^x - 2^(-x)) dx. - _Amiram Eldar_, Jul 16 2020
%e 0.79248125036057...
%t RealDigits[Log[4, 3], 10, 100][[1]] (* _Vincenzo Librandi_, Aug 30 2013 *)
%o (PARI) log(3)/log(4) \\ _Charles R Greathouse IV_, May 09 2016
%Y Cf. A010060.
%Y Cf. decimal expansion of log_4(m): this sequence, A153201 (m=5), A153460 (m=6), A153615 (m=7), A154155 (m=10), A154176 (m=11), A154197 (m=12), A154224 (m=13), A154464 (m=14), A154543 (m=15), A154849 (m=17), A154909 (m=18), A155004 (m=19), A155183 (m=20), A155545 (m=21), A155695 (m=22), A155818 (m=23), A155936 (m=24).
%K cons,nonn
%O 0,1
%A _Benoit Cloitre_, Jun 08 2004
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