A225665 Number of nonrepeating vectors in a counting procedure that starts with the digits of (n base 16).

6, 5, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 4, 3, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 2, 1, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 1, 2, 2, 6, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 4, 4, 4, 4, 6, 6, 8, 10, 12

Offset

0,1

Comments

The counting procedure and "eventually period 6 theorem" are introduced at A225660. Conjecture: if a(n) is odd for only finitely many n.

Links

Clark Kimberling, Table of n, a(n) for n = 0..10000

Example

To see that a(20) = 4, note that 20 = (14 in base 16), and write14 -> 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]; lst = Flatten[Table[a = {t = IntegerDigits[n, 16]}; While[Count[a, t] =!= 2, AppendTo[a, t = BinCounts[t, {0, Max[t] + 1, 1}]]]; First[Position[a, Last[a]]] - 1, {n, 0, 280}]]  (* Peter J. C. Moses, May 09 2013 *)

Crossrefs

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

Sequence in context: A225663 A225664 A349249 * A019686 A143304 A021157

Adjacent sequences: A225662 A225663 A225664 * A225666 A225667 A225668

Keyword

nonn,base

Author

Clark Kimberling, May 12 2013

Status

approved