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A321071
Twice the Thue-Morse constant (A014571).
0
8, 2, 4, 9, 0, 8, 0, 6, 7, 2, 8, 0, 2, 1, 5, 1, 9, 5, 5, 6, 6, 7, 2, 2, 7, 3, 6, 5, 1, 6, 9, 1, 0, 5, 6, 6, 1, 7, 8, 9, 5, 6, 7, 4, 8, 9, 1, 1, 5, 3, 9, 1, 1, 5, 1, 4, 6, 7, 5, 8, 8, 3, 0, 6, 9, 7, 5, 8, 7, 1, 8, 4, 7, 3, 1, 5, 6, 5, 1, 7, 7, 9, 2, 7, 6, 0, 9, 0, 8, 0
OFFSET
0,1
COMMENTS
This is the value of the g.f. of A010060 at x = 1/2. This number is transcendental.
FORMULA
Equals Sum_{k>=0} A010060(k)*2^(-k) = 1 - (Product_{k>=0} (1 - 2^(-2^k)))/2.
Equals Sum_{k>=1} 2^(-A000069(k)).
EXAMPLE
Equals 2^(-1) + 2^(-2) + 2^(-4) + 2^(-7) + ... = 0.11010011001011010..._2 = 0.82490806728021519...
MATHEMATICA
P = FromDigits[{ThueMorse /@ Range[0, 400], 0}, 2];
RealDigits[2P, 10, 105][[1]] (* Jean-François Alcover, Apr 21 2021 *)
PROG
(PARI) 1-prodinf(n=0, 1-1.>>2^n)/2
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Oct 27 2018
STATUS
approved