A225663 Number of nonrepeating vectors in a counting procedure that starts with the digits of (n base 5).

6, 5, 3, 4, 6, 4, 3, 0, 2, 4, 2, 1, 0, 2, 4, 1, 2, 2, 6, 4, 4, 4, 4, 4, 6, 2, 1, 1, 4, 4, 1, 0, 2, 4, 6, 1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 6, 4, 4, 6, 1, 0, 2, 4, 4, 1, 2, 2, 4, 4, 2, 2, 5, 4, 6, 4, 4, 4, 4, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

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

Cf. A225660 (base 2), A225664 (base 10), A225665 (base 16)

Sequence in context: A153330 A225661 A225662 * A225664 A349249 A225665

Adjacent sequences: A225660 A225661 A225662 * A225664 A225665 A225666

Keyword

nonn,base

Author

Clark Kimberling, May 12 2013

Status

approved