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%I #28 Jul 01 2023 14:15:58
%S 2,9,0,1,9,6,5,5,7,1,3,8,7,0,8,6,8,5,3,5,8,2,1,2,6,0,0,5,5,5,4,2,4,4,
%T 0,2,9,8,7,4,9,7,7,9,4,2,3,2,1,3,9,4,8,3,0,4,2,9,9,7,3,5,5,3,4,8,7,1,
%U 2,8,7,1,8,5,1,5,3,4,0,3,7,5,2,1,6,8,3,8,6,7,5,4,0,0,0,6,1,1,6,0,7,3,4,6,0
%N Decimal expansion of the infinite Fibonacci word, interpreted as a binary expansion.
%C That is to say, take A003849 (the morphism 0 -> 01 and 1 -> 0 starting from a single 0) and interpret it as a decimal fraction with the decimal point at the very beginning.
%C Davison shows that this constant is transcendental. - _Charles R Greathouse IV_, Feb 28 2014
%H J. L. Davison, <a href="http://www.jstor.org/stable/2041058">A series and its associated continued fraction</a>, Proc. Amer. Math. Soc. 63 (1977), pp. 29-32.
%H R. J. Mathar, <a href="/A228249/a228249.pdf">Gallery of walks on the square lattice by a Turing Plotter for binary sequences</a>(2013)
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 1 - 0.709803442861... = 1 - A014565. - _Joerg Arndt_, Aug 20 2013
%e 0.290196557138708685358212600555424402987497794232139483042997355348712...
%t RealDigits[ FromDigits[{Nest[Flatten[#/.{0 -> {0,1}, 1 -> {0}}]&,{0},12],0},2],10,111][[1]]
%o (PARI) c()=my(o=0,c=.25,L=default(realprecision)*2136\643,k=2,F); while((F=fibonacci(k++))<=L,[o,c]=[c,c+o>>F]); c \\ _Charles R Greathouse IV_, Feb 28 2014
%K nonn,cons
%O 0,1
%A _Robert G. Wilson v_, Aug 18 2013
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