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

Offset: 1

Author

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

Keywords

• nonn

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

• 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.