A092331 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 positive (but not necessarily all the same) length and F(y_i)=F(y_j) for all i,j<=k.

1, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 3, 4, 1, 3, 2, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 2, 5, 2, 2, 4, 3, 2, 5, 2, 3, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 3, 4, 3, 2, 3, 3, 2, 3, 4, 4, 3, 3, 5, 3, 3, 3, 4, 5, 3, 3, 3, 4, 3, 3, 5, 3, 6, 3, 3, 4, 6, 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 that the 'y' blocks count as being equivalent whenever the sum of their digits is equal.

Examples

			From _Rémy Sigrist_, Feb 08 2023: (Start)
The first terms, alongside an appropriate partition of prior terms, are:
  n   a(n)  Prior terms
  --  ----  -----------------
   1     1  N/A
   2     1  1
   3     2  1|1
   4     2  1 1|2
   5     3  1 1|2|2
   6     1  1 1 2 2 3
   7     2  1 1|2 2|3 1
   8     2  1 1 2 2|3 1 2
   9     3  1 1|2 2|3 1|2 2
  10     2  1|1 2 2 3|1 2 2 3
(End)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• 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].
• Rémy Sigrist, C program
• Index entries for sequences related to Gijswijt's sequence

Crossrefs

Cf. A090822, A091975, A091976.

Programs

C

See Links section.