A225661 - OEIS

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A225661

Number of nonrepeating vectors in a counting procedure that starts with the digits of (n base 3).

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

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OFFSET

0,1

COMMENTS

The counting procedure and "eventually period 6 theorem" are introduced at A225660. Conjecture: if a(n) > 6, then a(n) is odd.

LINKS

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

EXAMPLE

To see that a(2) = 3, write 2 -> 001 -> 21 -> 011 -> 12 -> 011, so that the 3 nonrepeating vectors are (2), (0,0,1), (2,1). After (2,1) the cycle (1,2) -> (0,1) has length 2, so that the remainder of the sequence of vectors is periodic with period 2, hence also period 6.

MATHEMATICA

Clear[a, t]; Flatten[Table[a = {t = IntegerDigits[n, 3]}; 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: A158038 A259281 A153330 * A225662 A225663 A225664

Adjacent sequences: A225658 A225659 A225660 * A225662 A225663 A225664

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, May 12 2013

STATUS

approved