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%I #15 Aug 02 2014 06:17:48
%S 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,
%T 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,
%U 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
%N Start with the sequence 2322322323222323223223 and extend by always appending the curling number (cf. A094004).
%C 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.
%C 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.
%C Note that a(362) = 4. The sequence is unbounded, but a(n) = 5 is not reached until about n = 10^(10^23) - see A090822.
%H N. J. A. Sloane, <a href="/A116909/b116909.txt">Table of n, a(n) for n = 1..500</a>
%H F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
%H 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 [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>].
%H N. J. A. Sloane, <a href="/A116909/a116909.f.txt">Fortran program</a>
%H <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%Y Cf. A094004, A090822, A174998. Sequence of run lengths: A161223.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_, Jan 15 2009, based on email from _Benjamin Chaffin_, Apr 09 2008 and Dec 04 2009