A217437 Number of strings of length n in {2,3}* for which at least one of tail(2 S) > tail(S) and tail(3 S) > tail(S) holds.

2, 1, 2, 1, 5, 3, 12, 9, 19, 16, 38, 20, 59, 42, 104, 65, 213, 111, 400, 245, 765, 439, 1563, 820, 3046, 1731, 5955, 3292, 12078, 6343, 23841, 13090, 47204, 25534, 95140, 50154

Offset: 1

Author

Benjamin Chaffin, Oct 02 2012

Keywords

• nonn
• more

Comments

The "curling number" k = k(S) of a string of numbers S = s(1), ..., s(m) is defined as follows. Write S as XY^k for strings 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 S.

The "tail length" tail(S) of S is defined as follows: start with S and repeatedly append the curling number (recomputing it at each step) until a 1 is reached; tail(S) is the number of terms that are appended to S before a 1 is reached.

No example is known where both tail(2 S) > tail(S) and tail(3 S) > tail(S) hold.

Examples

			Tail(22322)=2, tail(222322)=8, tail(322322)=2, so 22322 is counted in a(5).
		

Links

• 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.

Extensions

a(31)-a(36) from Lars Blomberg, Nov 01 2016