A092333 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 of positive (but not necessarily equal) length and for any i=F(y_(i+1)).

1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 7, 8, 6, 7, 7, 8, 8, 9, 8, 9, 8, 9, 9, 10, 9, 10, 8, 9, 9, 10, 10, 11, 9, 10, 10, 11, 11, 12, 10, 11, 11, 12, 12, 13, 11, 12, 12, 13, 13, 14, 10, 11, 11, 12, 12, 13, 11, 12, 12, 13, 13, 14, 13, 14, 13, 14

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 accept 'y' blocks as upholding Gijswijt's axiom whenever they satisfy the inequality above.

Question: Is there any integer U such that a(M)<=a(M+1) for all M>U?

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.