cp's OEIS Frontend

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

%I A316828 #22 May 27 2025 10:09:39
%S A316828 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 A316828 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 A316828 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 A316828 Image of the Thue-Morse sequence A010060 under the morphism {1 -> 1,2; 0 -> 0,2}.
%C A316828 The morphism is applied just once.
%C A316828 This is a word that is pure morphic and uniform primitive morphic, but neither pure uniform morphic nor pure primitive morphic.
%C A316828 A010060 interleaved with A007395. - _Antti Karttunen_, Oct 08 2018
%H A316828 Antti Karttunen, <a href="/A316828/b316828.txt">Table of n, a(n) for n = 0..65537</a>
%H A316828 Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, and Luca Q. Zamboni, <a href="https://arxiv.org/abs/1711.10807">A Taxonomy of Morphic Sequences</a>, arXiv:1711.10807 [cs.FL], 2017.
%F A316828 If n is odd, a(n) = 2, otherwise a(n) = A010060(n/2). - _Antti Karttunen_, Oct 08 2018
%t A316828 Riffle[ThueMorse[Range[0,100]],2] (* _Paolo Xausa_, Dec 18 2023 *)
%o A316828 (PARI) A316828(n) = if(n%2,2,hammingweight(n/2)%2); \\ _Antti Karttunen_, Oct 08 2018
%Y A316828 Cf. A010060.
%Y A316828 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 A316828 nonn
%O A316828 0,2
%A A316828 _N. J. A. Sloane_, Jul 14 2018