A092335 - OEIS

%I #10 Aug 02 2014 06:17:47

%S 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,

%T 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,

%U 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

%N 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).

%C 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

%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.

%H 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 [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].

%H <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a>

%e 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]

%Y Cf. A090822, A091975, A091976.

%K nonn

%O 1,3

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