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a(1) = a(2) = 1; for n > 1, a(n+1) = largest integer k such that the word a(1)a(2)...a(n-1) is of the form xy^k for words x and y (where y has positive length), i.e., the maximal number of repeating blocks at the end of the sequence so far.
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%I #14 Jul 28 2017 23:50:46

%S 1,1,1,2,3,1,1,1,2,3,1,2,2,1,2,1,1,2,2,1,2,1,1,2,2,2,2,3,4,1,1,1,2,3,

%T 1,1,1,2,3,1,2,2,1,2,1,1,2,2,1,2,1,1,2,2,2,2,3,4,1,2,2,1,2,1,1,2,2,1,

%U 2,1,1,2,2,2,2,3,4,1,2,2,2,2,3,4,1,2,2,2,2,3,4,2,3,1,1,1,2,3,1,1,1

%N a(1) = a(2) = 1; for n > 1, a(n+1) = largest integer k such that the word a(1)a(2)...a(n-1) is of the form xy^k for words x and y (where y has positive length), i.e., the maximal number of repeating blocks at the end of the sequence so far.

%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/VOL10/Sloane/sloane55.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/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>

%Y Cf. A090822.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, May 31 2004