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%I #23 Jun 23 2024 06:39:41
%S 0,1,2,3,1,0,2,3,0,1,3,2,1,0,2,3,0,1,2,3,1,0,3,2,0,1,3,2,1,0,2,3,0,1,
%T 2,3,1,0,2,3,0,1,3,2,1,0,3,2,0,1,2,3,1,0,3,2,0,1,3,2,1,0,2,3,0,1,2,3,
%U 1,0,2,3,0,1,3,2,1,0,2,3,0,1,2,3,1,0,3
%N An infinite sequence over {0,1,2,3} without palindromes of length more than 1.
%C A palindrome is a block that reads the same forwards and backwards.
%H Kevin Ryde, <a href="/A372257/b372257.txt">Table of n, a(n) for n = 0..10000</a>
%H Jean Berstel, Luc Boasson, Olivier Carton, and Isabelle Fagnot, <a href="https://arxiv.org/abs/0903.2382">Infinite words without palindrome</a>, arXiv:0903.2382 [cs.DM], March 13 2009, section 2 word "x".
%F Generated by iterating the morphism 0->01, 1->23, 2->45, 3->23, 4->01, 5->67, 6->45, 7->67, followed by coding 0->0, 1->1, 2->2, 3->3, 4->1, 5->0, 6->3, 7->2.
%F a(n) = (n mod 4) XOR A014707(floor(n/2)), using bitwise XOR, by noting the morphism before coding is (n mod 4) + 4*A014707(floor(n/2)). - _Kevin Ryde_, Apr 26 2024
%o (PARI) a(n) = bitxor(bitand(n,3), bittest(n, valuation(n>>1+1,2)+2)); \\ _Kevin Ryde_, Apr 26 2024
%Y Cf. A014707, A372258 (mod 2), A369989.
%K nonn,easy
%O 0,3
%A _Jeffrey Shallit_, Apr 24 2024
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