A093371 - OEIS

%I #31 Jul 28 2017 23:45:25

%S 1,1,2,3,6,10,20,37,74,143,286,562,1124,2230,4460,8884,17768,35465,

%T 70930,141720,283440,566600,1133200,2265843,4531686,9062261,18124522,

%U 36246826,72493652,144982872

%N Start with any initial string of n numbers s(1), ..., s(n), with s(1) = 2, other s(i)'s = 2 or 3 (so there are 2^(n-1) starting strings). The rule for extending the string is this as follows: To get s(n+1), write the string s(1)s(2)...s(n) as xy^k for words x and y (where y has positive length) and k is maximized, i.e., k = the maximal number of repeating blocks at the end of the sequence. Then a(n) = number of starting strings for which k = 1.

%C See A122536 for many more terms. - _N. J. A. Sloane_, Oct 25 2012

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

%F a(n) = 2^(n-1) - A093370(n).

%Y Cf. A093370, A093369, A090822, A216955, A216956.

%Y Equals A122536/2. - _N. J. A. Sloane_, Sep 25 2012

%Y Different from, but easily confused with, A007148 and A045690.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Apr 28 2004

%E More terms from _N. J. A. Sloane_, Sep 26 2012