A372257 An infinite sequence over {0,1,2,3} without palindromes of length more than 1.

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, 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, 1, 0, 2, 3, 0, 1, 3, 2, 1, 0, 2, 3, 0, 1, 2, 3, 1, 0, 3

Offset

0,3

Comments

A palindrome is a block that reads the same forwards and backwards.

Links

Kevin Ryde, Table of n, a(n) for n = 0..10000

Jean Berstel, Luc Boasson, Olivier Carton, and Isabelle Fagnot, Infinite words without palindrome, arXiv:0903.2382 [cs.DM], March 13 2009, section 2 word "x".

Formula

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.

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

Prog

(PARI) a(n) = bitxor(bitand(n, 3), bittest(n, valuation(n>>1+1, 2)+2)); \\ Kevin Ryde, Apr 26 2024

Crossrefs

Cf. A014707, A372258 (mod 2), A369989.

Sequence in context: A368495 A189117 A365196 * A253580 A020921 A293113

Adjacent sequences: A372254 A372255 A372256 * A372258 A372259 A372260

Keyword

nonn,easy,changed

Author

Jeffrey Shallit, Apr 24 2024

Status

approved