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A092332
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For S a string of numbers, let F(S) = the product of those numbers. Let a(1)=1. For n>1, a(n) is the greatest k such that 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 of positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k.
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0
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1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 4, 2, 2, 3, 2, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 2, 4, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 4, 4, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 4, 4, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 2, 2, 3, 4, 3, 3, 2, 2, 4, 3, 5, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1
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OFFSET
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1,3
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COMMENTS
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Here [x][y] denotes concatenation of strings. This is Gijswijt's sequence, A090822, except that the 'y' blocks count as being equivalent whenever the product of their digits is the same.
For actually calculating this sequence, compare prime compositions of the products, not the products themselves, as those grow far too fast.
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LINKS
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Table of n, a(n) for n=1..105.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and _Allan 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 _Allan Wilks_, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
Index entries for sequences related to Gijswijt's sequence
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CROSSREFS
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Cf. A090822, A091975, A091976.
Sequence in context: A153904 A128762 A126307 * A092334 A047060 A050167
Adjacent sequences: A092329 A092330 A092331 * A092333 A092334 A092335
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KEYWORD
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nonn
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AUTHOR
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J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004
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STATUS
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approved
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