A092334 For S a finite string of numbers, let M(S) denote the maximal number among them. Let a(1)=1. For n>1, a(n) is the greatest 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 of positive (but not necessarily equal) length and M(y_i)=M(y_j) for all i,j.

1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 4, 3, 3, 3, 3, 4, 4, 5, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 2, 2

Offset: 1

Author

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

Keywords

• nonn

Comments

Here multiplication denotes concatenation of strings. This is Gijswijt's sequence, A090822, except we count 'y' blocks as being equivalent as long as their maximal elements are identical.

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.