A228249 - OEIS

A228249

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

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

(list; constant; graph; refs; listen; history; text; internal format)

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 fraction with the decimal 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. 29-32.

R. J. Mathar, Gallery of walks on the square lattice by a Turing Plotter for binary sequences(2013)

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