A116909 Start with the sequence 2322322323222323223223 and extend by always appending the curling number (cf. A094004).

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

Offset: 1

Author

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

Keywords

• nonn
• nice

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.