A372258 An infinite sequence over {0,1} with no palindromes of length > 12.

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

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 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)

First difference, taken modulo 2, of the paperfolding sequence with unfolding instructions 001111.... . - Jeffrey Shallit, Dec 29 2024

Prog

(PARI) a(n) = bitxor(bitand(n, 1), bittest(n, valuation(n>>1+1, 2)+2)); \\ Kevin Ryde, Apr 28 2024

Crossrefs

Cf. A014707, A369989, A372257.

Sequence in context: A286685 A284878 A118006 * A285196 A189673 A189014

Adjacent sequences: A372255 A372256 A372257 * A372259 A372260 A372261

Keyword

nonn,easy,changed

Author

Jeffrey Shallit, Apr 24 2024

Status

approved