%I #17 Dec 18 2023 17:03:44

%S 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,

%T 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,

%U 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

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

%C The morphism is applied just once.

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

%C A010060 interleaved with A007395. - _Antti Karttunen_, Oct 08 2018

%H Antti Karttunen, <a href="/A316828/b316828.txt">Table of n, a(n) for n = 0..65537</a>

%H Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, <a href="https://arxiv.org/pdf/1711.10807.pdf">A Taxonomy of Morphic Sequences</a>, arXiv preprint arXiv:1711.10807, Nov 29 2017

%F If n is odd, a(n) = 2, otherwise a(n) = A010060(n/2). - _Antti Karttunen_, Oct 08 2018

%t Riffle[ThueMorse[Range[0,100]],2] (* _Paolo Xausa_, Dec 18 2023 *)

%o (PARI) A316828(n) = if(n%2,2,hammingweight(n/2)%2); \\ _Antti Karttunen_, Oct 08 2018

%Y Cf. A010060.

%Y 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.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jul 14 2018