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

0,1

COMMENTS

This is the value of the g.f. of A010060 at x = 1/2. This number is transcendental.

LINKS

Table of n, a(n) for n=0..89.

Eric Weisstein's World of Mathematics, Thue-Morse Constant

Index entries for transcendental numbers

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

Cf. A000069, A001969, A010060, A014571.

Sequence in context: A245533 A021552 A245279 * A008830 A248302 A217294

Adjacent sequences:  A321068 A321069 A321070 * A321072 A321073 A321074

KEYWORD

nonn,cons

AUTHOR

Jianing Song, Oct 27 2018

STATUS

approved

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Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)