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A372258
An infinite sequence over {0,1} with no palindromes of length > 12.
3
0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1
OFFSET
0
COMMENTS
A palindrome is a block that reads the same forwards and backwards.
LINKS
Jean Berstel, Luc Boasson, Olivier Carton, and Isabelle Fagnot, Infinite words without palindrome, arXiv:0903.2382 [cs.DM], March 13 2009, section 3 word "z".
FORMULA
Generated by iterating the morphism 0->01, 1->21, 2->34, 3->01, 4->54, 5->34, followed by the coding n->n mod 2.
From Kevin Ryde, Apr 28 2024: (Start)
a(n) = A372257(n) mod 2.
a(n) = (n + A014707(floor(n/2))) mod 2 [per Berstel et al section 4, but misprint there "word y" should be "word z"]. (End)
PROG
(PARI) a(n) = bitxor(bitand(n, 1), bittest(n, valuation(n>>1+1, 2)+2)); \\ Kevin Ryde, Apr 28 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jeffrey Shallit, Apr 24 2024
STATUS
approved