OFFSET
0,1
COMMENTS
The counting procedure and "eventually period 6 theorem" are introduced at A225660.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..299
EXAMPLE
To see that a(3) = 10, write 3! = 6 -> 0000001 -> 61 -> 0100001-> 52 -> 001001 -> 42 -> 00101 -> 32 -> 0011 -> 22 -> 001 -> 201 -> 111 -> 03 -> 1001 -> 22. This shows that the 10 nonrepeating vectors are (6), (0,0,0,0,0,0,1), (6,1), ... ,and (0,0,1,1). After (0,0,1,1) the cycle (2,2) -> ... -> (2,2) has length 6, so that the remainder of the sequence of vectors is periodic with period 6.
MATHEMATICA
Clear[a, t]; Flatten[Table[a = {t = IntegerDigits[n!]}; While[Count[a, t] =!= 2, AppendTo[a, t = BinCounts[t, {0, Max[t] + 1, 1}]]]; First[Position[a, Last[a]]] - 1, {n, 0, 180}]] (* Peter J. C. Moses, May 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 15 2013
STATUS
approved