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A303581
Add i (>= 0) to the i-th block of terms in the Thue-Morse sequence A010060.
1
0, 2, 3, 2, 4, 3, 3, 4, 5, 4, 4, 5, 4, 5, 5, 4, 6, 5, 5, 6, 5, 6, 6, 5, 5, 6, 6, 5, 6, 5, 5, 6, 7, 6, 6, 7, 6, 7, 7, 6, 6, 7, 7, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 6, 6, 7, 7, 6, 6, 7, 6, 7, 7, 6, 8, 7, 7, 8, 7, 8, 8, 7, 7, 8, 8, 7, 8, 7, 7, 8, 7, 8, 8, 7, 8, 7, 7
OFFSET
0,2
COMMENTS
Constructed with a view to obtaining a musically more interesting version of the Thue-Morse sequence. (This was not a success.)
LINKS
EXAMPLE
The initial blocks of A010060 are
0, 1, 1,0, 1,0,0,1, 1,0,0,1,0,1,1,0, 1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1, ...
and we add 0, 1, 2, ... to the terms in these blocks to obtain
0, 2, 3,2, 4,3,3,4, 5,4,4,5,4,5,5,4, 6,5,5,6,5,6,6,5,5,6,6,5,6,5,5,6, ...
PROG
(PARI) a(n) = hammingweight(n)%2 + #binary(n) \\ Rémy Sigrist, Nov 11 2020
(Python)
def A303581(n): return (n.bit_count()&1)+n.bit_length() # Chai Wah Wu, Mar 02 2023
CROSSREFS
Cf. A010060.
Compare the Danish composer Per Nørgård's infinity series A004718.
Sequence in context: A246348 A205782 A070296 * A216647 A072645 A316714
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 10 2018
EXTENSIONS
More terms from Rémy Sigrist, Nov 11 2020
STATUS
approved