A092335 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 and equal length and for any i,j, y_i and y_j agree at every other term starting from the left (see example).

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

Offset

1,3

Comments

Multiplication here denotes concatenation of strings. This is Gijswijt's sequence, A090822, except when checking if 'y' blocks are 'equal', we only compare every other term and ignore the others

Links

Table of n, a(n) for n=1..105.

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

Example

For example, [1 2 3 4 5] and [1 0 3 100 5] count as being equal because both are of the form [1 ? 3 ? 5]

Crossrefs

Cf. A090822, A091975, A091976.

Sequence in context: A151902 A094839 A341771 * A278912 A339186 A302479

Adjacent sequences: A092332 A092333 A092334 * A092336 A092337 A092338

Keyword

nonn

Author

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

Status

approved