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Search: id:A091787
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| A091787 |
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a(1) = 2. To get a(n+1), write the string a(1)a(2)...a(n) as xy^k for words x and y (where y has positive length) and k is maximized, i.e. k = the maximal number of repeating blocks at the end of the sequence so far. Then a(n+1) = max(k,2). |
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18
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| 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Here xy^k means the concatenation of the words x and k copies of y.
a(77709404388415370160829246932345692180) = 5 is the first time 5 appears.
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REFERENCES
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N. J. A. Sloane, Seven Staggering Sequences, in Homage to a Pied Puzzler, E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-110.
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LINKS
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F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and A. R. Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
N. J. A. Sloane, Seven Staggering Sequences.
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EXAMPLE
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To get a(2): a(1) = 2 = (2)^1, so k = 1, a(2) = 2. To get a(3): a(1)a(2) = 22 = (2)^2, so a(3) = k = 2. To get a(4): a(1)a(2)a(3) = 222 = (2)^3, so a(3) = k = 3.
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CROSSREFS
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Cf. A090822, A091799.
Sequence in context: A156384 A064656 A056608 this_sequence A087040 A065569 A127656
Adjacent sequences: A091784 A091785 A091786 this_sequence A091788 A091789 A091790
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 07 2004
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