A316828 Image of the Thue-Morse sequence A010060 under the morphism {1 -> 1,2; 0 -> 0,2}.

0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2

Offset: 0

Author

N. J. A. Sloane, Jul 14 2018

Keywords

• nonn

Comments

The morphism is applied just once.

This is a word that is pure morphic and uniform primitive morphic, but neither pure uniform morphic nor pure primitive morphic.

A010060 interleaved with A007395. - Antti Karttunen, Oct 08 2018

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, and Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv:1711.10807 [cs.FL], 2017.

Crossrefs

Cf. A010060.

Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

Programs

Mathematica

Riffle[ThueMorse[Range[0,100]],2] (* Paolo Xausa, Dec 18 2023 *)

PARI

A316828(n) = if(n%2,2,hammingweight(n/2)%2); \\ Antti Karttunen, Oct 08 2018

Formula

If n is odd, a(n) = 2, otherwise a(n) = A010060(n/2). - Antti Karttunen, Oct 08 2018