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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..36.

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: A109087 A102048 A102551 * A152823 A086545 A126083

Adjacent sequences:  A217434 A217435 A217436 * A217438 A217439 A217440

KEYWORD

nonn,more

AUTHOR

Benjamin Chaffin, Oct 02 2012

EXTENSIONS

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

STATUS

approved

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Last modified May 22 21:40 EDT 2017. Contains 286906 sequences.