

A228249


The decimal expansion of the infinite Fibonacci word, interpreted as a binary expansion.


0



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, 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, 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
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OFFSET

0,1


COMMENTS

That is to say, take A003849 (the morphism 0 > 01 and 1 > 0 starting from a single 0) and interpret it as a decimal with the point at the very beginning.
Davison shows that this constant is transcendental.  Charles R Greathouse IV, Feb 28 2014


LINKS

Table of n, a(n) for n=0..104.
J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), pp. 2932.
Richard J. Mathar, Gallery of Walks on the Square Lattice by a Turing Plotter for Binary Sequences
Index entries for transcendental numbers


FORMULA

Equals 1  0.709803442861... = 1  A014565.  Joerg Arndt, Aug 20 2013


EXAMPLE

0.290196557138708685358212600555424402987497794232139483042997355348712...


MATHEMATICA

RealDigits[ FromDigits[{Nest[Flatten[#/.{0 > {0, 1}, 1 > {0}}]&, {0}, 12], 0}, 2], 10, 111][[1]]


PROG

(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


CROSSREFS

Sequence in context: A127558 A324330 A197294 * A011063 A021779 A201893
Adjacent sequences: A228246 A228247 A228248 * A228250 A228251 A228252


KEYWORD

nonn,cons


AUTHOR

Robert G. Wilson v, Aug 18 2013


STATUS

approved



