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A116909 Start with the sequence 2322322323222323223223 and extend by always appending the curling number (cf. A094004). 5
2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The (unproved) Curling Number Conjecture is that any starting sequence eventually leads to a "1". The starting sequence used here extends for a total of 142 steps before reaching 1. After than it continues as A090822.

Benjamin Chaffin has found that in a certain sense this is the best of all 2^45 starting sequences of at most 44 2's and 3's.

Note that a(362) = 4. The sequence is unbounded, but a(n) = 5 is not reached until about n = 10^(10^23) - see A090822.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..500

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].

N. J. A. Sloane, Fortran program

Index entries for sequences related to curling numbers

CROSSREFS

Cf. A094004, A090822, A174998. Sequence of run lengths: A161223.

Sequence in context: A143393 A269111 A166497 * A182006 A085239 A242872

Adjacent sequences:  A116906 A116907 A116908 * A116910 A116911 A116912

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Jan 15 2009, based on email from Benjamin Chaffin, Apr 09 2008 and Dec 04 2009

STATUS

approved

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Last modified January 18 05:30 EST 2019. Contains 319269 sequences. (Running on oeis4.)