A092332 - OEIS

A092332

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.

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

1,3

COMMENTS

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.

LINKS

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

CROSSREFS

Cf. A090822, A091975, A091976.

Sequence in context: A096396 A126307 A320838 * A092334 A269971 A276605

Adjacent sequences: A092329 A092330 A092331 * A092333 A092334 A092335

KEYWORD

nonn

AUTHOR

J. Taylor (integersfan(AT)yahoo.com), Mar 17 2004

STATUS

approved