A019299 - OEIS

%I #20 Jan 31 2023 16:02:56

%S 1,2,4,9,18,37,75,150,300,601,1203,2406,4813,9626,19252,38505,77010,

%T 154021,308043,616086,1232173,2464346,4928692,9857385,19714771,

%U 39429542,78859084,157718169,315436338,630872677,1261745355,2523490710,5046981420

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

%F a(n) = Sum_{k=0..n} (1+(-1)^A010060(n-k))*2^k/2. - _Paul Barry_, Jan 06 2005

%F From _Lorenzo Sauras Altuzarra_, Jan 31 2023: (Start)

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

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

%p a:= n-> add((1+(-1)^irem(add(j, j=convert(n-i, base, 2)), 2))*2^i/2, i=0..n):

%p seq(a(n), n=0..32); # _Lorenzo Sauras Altuzarra_, Jan 31 2023

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

%K nonn

%O 0,2

%A _Jonas Wallgren_