A019299 First n elements of Thue-Morse sequence A010059 read as a binary number.

1, 2, 4, 9, 18, 37, 75, 150, 300, 601, 1203, 2406, 4813, 9626, 19252, 38505, 77010, 154021, 308043, 616086, 1232173, 2464346, 4928692, 9857385, 19714771, 39429542, 78859084, 157718169, 315436338, 630872677, 1261745355, 2523490710, 5046981420

Offset: 0

Author

Jonas Wallgren

Keywords

• nonn

Crossrefs

Cf. A001969 (evil numbers), A010060, A014571, A125050.

Programs

Maple

a:= n-> add((1+(-1)^irem(add(j, j=convert(n-i, base, 2)), 2))*2^i/2, i=0..n):
seq(a(n), n=0..32); # Lorenzo Sauras Altuzarra, Jan 31 2023

Formula

a(n) = Sum_{k=0..n} (1+(-1)^A010060(n-k))*2^k/2. - Paul Barry, Jan 06 2005

From Lorenzo Sauras Altuzarra, Jan 31 2023: (Start)

a(n+1) = 2*a(n) + 1 if a(n) is evil; a(n+1) = 2*a(n) otherwise (see also A125050).

a(n) = floor((1-c)*2^(n+1)), where c = A014571 is the Thue - Morse constant. (End)