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Search: id:A093340
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| A093340 |
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a(n) = length of longest string that can be generated by a starting string of 2's and 3's of length n, using the rule described in the Comments lines. |
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+0
3
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| 1, 4, 4, 8, 9, 14, 15, 66, 68, 70, 123, 123, 125, 132, 133, 134, 135, 136, 138, 139
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Start with an initial string of n numbers s(1), ..., s(n), all = 2 or 3, with s(1) = 2. The rule for extending the string is this:
To get s(i+1), write the string s(1)s(2)...s(i) 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 s(i+1) = k if k >=2, but if k=1 you must stop (without writing down the 1).
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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].
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EXAMPLE
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a(4) = 8, using the starting string 2,3,2,3, which extends to 2,3,2,3,2,2,2,3 of length 8.
a(8) = 66: start = 23222323, end = 232223232223222322322232223232223222322322232223232223222322322332.
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CROSSREFS
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Cf. A091787, A090822, A093369, A094004, A094005.
Adjacent sequences: A093337 A093338 A093339 this_sequence A093341 A093342 A093343
Sequence in context: A053249 A071339 A101921 this_sequence A046558 A014687 A004024
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KEYWORD
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nonn,more,nice
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AUTHOR
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njas, Apr 26 2004
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