A093370 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.

0, 1, 2, 5, 10, 22, 44, 91, 182, 369, 738, 1486, 2972, 5962, 11924, 23884, 47768, 95607, 191214, 382568, 765136, 1530552, 3061104, 6122765, 12245530, 24492171, 48984342, 97970902, 195941804, 391888040

Offset: 1

Author

N. J. A. Sloane, Apr 28 2004

Keywords

• nonn

Examples

			For n=2 there are 2 starting strings, 22 and 23 and only the first has k > 1.
For n=4 there are 8 starting strings, but only 5 have k > 1, namely 2222, 2233, 2322, 2323, 2333.
		

Links

• 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].
• B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102 [math.CO], Dec 25 2012.
• B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3.
• Index entries for sequences related to Gijswijt's sequence
• Index entries for sequences related to curling numbers

Crossrefs

Cf. A090822, A093369, A093371, A121880, A122536.

Formula

Equals A121880(n)/2, or 2^(n-1) - A122536(n)/2.

a(n)/2^(n-1) seems to converge to a number around 0.73.

Extensions

More terms from Sarah Nibs, via A122536, Sep 18 2006