OFFSET
0,1
COMMENTS
The counting procedure and "eventually period 6 theorem" are introduced at A225660. Conjecture: if a(n) > 8, then a(n) is odd.
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..10000
EXAMPLE
To see that a(9) = 4, note that 9 = (14 in base 4), and write 14 -> 01011 -> 32 -> 0011-> 22 -> 002 -> 201 -> 111 -> 03 -> 1001 -> 22. This shows that the 4 nonrepeating vectors are (1,4), (0,1,0,1,1), (3,2), 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, 5]};
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,base
AUTHOR
Clark Kimberling, May 12 2013
STATUS
approved