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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.
0
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
1,1
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.
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.
EXAMPLE
Tail(22322)=2, tail(222322)=8, tail(322322)=2, so 22322 is counted in a(5).
CROSSREFS
Sequence in context: A102048 A318360 A102551 * A152823 A324605 A086545
KEYWORD
nonn,more
AUTHOR
Benjamin Chaffin, Oct 02 2012
EXTENSIONS
a(31)-a(36) from Lars Blomberg, Nov 01 2016
STATUS
approved