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A214216 List of minimal forbidden subwords of the Fibonacci word A003482. 2
22, 111, 21212, 11211211, 2121121211212, 112112121121121211211, 2121121211211212112121121121211212, 1121121211211212112121121121211211212112121121121211211, 21211212112112121121211211212112112121121211211212112121121121211211212112121121121211212 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A083123 A084017 A089184 * A079466 A217086 A079676
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 10 2012
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)