A094916 a(1) = 1; for n > 1, a(n) = curling number of (b(1),...,b(n-1)), where b() = Fibonacci word A003849 (with offset changed to 1).

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

Offset: 1

Author

N. J. A. Sloane, Jun 18 2004

Keywords

• nonn
• easy

Comments

The curling number of a finite string S = (s(1),...,s(n)) is the largest integer k such that S can be written as xy^k for strings x and y (where y has positive length).

Examples

			b(1) to b(12) are 0,1,0,0,1,0,1,0,0,1,0,0, which we can write as xy^2 with x = 0,1,0,0,1,0 and y = 1,0,0; and no greater k is possible, so a(12) = 2.
		

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].
• Index entries for sequences related to Gijswijt's sequence

Crossrefs

Cf. A090822, A003849, A093914, A093921.

Extensions

More terms from David Wasserman, Jul 03 2007