A303581 Add i (>= 0) to the i-th block of terms in the Thue-Morse sequence A010060.

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

Rémy Sigrist, Table of n, a(n) for n = 0..8192

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

Adjacent sequences: A303578 A303579 A303580 * A303582 A303583 A303584

Keyword

nonn

Author

N. J. A. Sloane, May 10 2018

Extensions

More terms from Rémy Sigrist, Nov 11 2020

Status

approved