|
|
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
|
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].
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|