A214216 List of minimal forbidden subwords of the Fibonacci word A003482.

22, 111, 21212, 11211211, 2121121211212, 112112121121121211211, 2121121211211212112121121121211212, 1121121211211212112121121121211211212112121121121211211, 21211212112112121121211211212112112121121211211212112121121121211211212112121121121211212

Offset

1,1

Comments

If S is one of the terms of this sequence, then no word RS can appear as a subword of A003482.

Or, make a list of all words in {1,2}* that do not appear as factors of A003482 and discard any word which has a shorter word on the list as a right factor.

All the terms are palindromes.

Complementing the first and last digits of each term gives (essentially) A214217.

Links

Table of n, a(n) for n=1..9.

A. de Luca, Subwords of the Fibonacci word, MathOverflow, April 9, 2011.

F. Mignosi, A. Restivo, M. Sciortino, Words and forbidden factors, WORDS (Rouen, 1999). Theoret. Comput. Sci. 273 (2002), no. 1-2, 99--117. MR1872445 (2002m:68096).

Formula

To get a(n), take A106750(n+2), delete last two digits, producing a palindrome P, say. Then a(n) = 1P1 if n is odd, or 2P2 if n is even.

Example

A106750(3)=121 -> P=1 -> 111 = a(1).
A106750(4)=12112 -> P=121 -> 2121 = a(2).
A106750(5)=12112121 -> P=121121 -> 11211211 = a(3).

Crossrefs

Cf. A003842, A106750, A213975, A214217.

Sequence in context: A083123 A084017 A089184 * A079466 A217086 A079676

Adjacent sequences: A214213 A214214 A214215 * A214217 A214218 A214219

Keyword

nonn

Author

N. J. A. Sloane, Jul 10 2012

Status

approved