A216951 Let S be a string of n 2's and 3's, with curling number k, which means S = XY^k where k is maximized; a(n) = number of S for which X must be taken to be the empty string.

2, 2, 2, 4, 2, 8, 2, 10, 8, 14, 2, 40, 2, 40, 32, 88, 2, 192, 2, 324, 100, 564, 2, 1356, 32, 2226, 370, 4564, 2, 9656, 2, 17944, 1450, 35424, 152, 74182, 2, 141628, 5774, 284342, 2, 578022, 2, 1134518, 23576, 2265394, 2, 4580468, 128, 9062280, 92236, 18129626

Offset

1,1

Comments

See A216730 for definition of curling number.

Links

Lars Blomberg, Table of n, a(n) for n = 1..120

B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102, 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 curling numbers

Example

For n=6, there are 8 strings S that satisfy the condition:
222222, k=6, Y=2
223223, k=2, Y=223
232232, k=2, Y=232
232323, k=3, Y=23
and 4 more by exchanging 2 and 3. Note that 233233 with k=2 is not on the list, because we could choose X empty, Y=233 or X=2332, Y=3, and the latter avoids taking X to be empty.

Crossrefs

Cf. A216730, A216952.

Sequence in context: A278242 A035580 A135293 * A366628 A320305 A064025

Adjacent sequences: A216948 A216949 A216950 * A216952 A216953 A216954

Keyword

nonn

Author

N. J. A. Sloane, Sep 24 2012

Extensions

More terms from Lars Blomberg, Nov 02 2016

Status

approved