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A092331
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For S a string of numbers, let F(S) = the sum of those numbers. Let a(1)=1. For n>1, a(n) is the largest k such that the string a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k], where each y_i is positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k.
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2
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1, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 3, 4, 1, 3, 2, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 2, 5, 2, 2, 4, 3, 2, 5, 2, 3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 3, 4, 3, 2, 3, 3, 2, 3, 4, 4, 3, 3, 5, 3, 3, 3, 4, 5, 3, 3, 3, 4, 3, 3, 5, 3, 6, 3, 3, 4, 6, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Here multiplication denotes concatenation of strings. This is Gijswijt's sequence, A090822, except that the 'y' blocks count as being equivalent whenever the sum of their digits is equal.
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LINKS
| 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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CROSSREFS
| Cf. A090822, A091975, A091976.
Sequence in context: A051521 A171810 A097028 * A200747 A089293 A034968
Adjacent sequences: A092328 A092329 A092330 * A092332 A092333 A092334
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KEYWORD
| nonn
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AUTHOR
| J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004
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