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A019299
First n elements of Thue-Morse sequence A010059 read as a binary number.
1
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
0,2
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)
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
CROSSREFS
Cf. A001969 (evil numbers), A010060, A014571, A125050.
Sequence in context: A081253 A118255 A206927 * A052932 A018097 A327738
KEYWORD
nonn
STATUS
approved