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

1,3

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.

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

Example

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)

Prog

(C) See Links section.

Crossrefs

Cf. A090822, A091975, A091976.

Sequence in context: A351258 A097028 A289442 * A299029 A200747 A328481

Adjacent sequences: A092328 A092329 A092330 * A092332 A092333 A092334

Keyword

nonn

Author

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

Status

approved