A321071 Twice the Thue-Morse constant (A014571).

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.

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.8, p. 437.

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