A225666 Number of nonrepeating vectors in a counting procedure that starts with the digits of n!.

5, 5, 3, 10, 4, 1, 8, 6, 6, 8, 6, 8, 8, 8, 10, 8, 10, 8, 8, 7, 9, 7, 7, 8, 9, 9, 7, 9, 9, 9, 9, 7, 9, 7, 9, 9, 9, 13, 15, 11, 9, 15, 13, 11, 9, 13, 17, 9, 13, 11, 23, 21, 19, 17, 19, 21, 15, 23, 19, 23, 19, 37, 25, 25, 23, 23, 27, 27, 33, 23, 21, 33, 27, 53

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

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

Sequence in context: A273826 A213054 A232609 * A365078 A175505 A158274

Adjacent sequences: A225663 A225664 A225665 * A225667 A225668 A225669

Keyword

nonn

Author

Clark Kimberling, May 15 2013

Status

approved