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A225662
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Number of nonrepeating vectors in a counting procedure that starts with the digits of (n base 4).
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1
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6, 5, 3, 4, 4, 3, 0, 2, 2, 1, 0, 2, 1, 2, 2, 6, 2, 1, 1, 4, 1, 0, 2, 4, 1, 2, 2, 4, 4, 4, 4, 4, 1, 0, 2, 4, 1, 2, 2, 4, 2, 2, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 3, 0, 3, 4, 1, 3, 3, 4, 3, 3, 3, 6, 4, 4, 6, 4, 1, 3, 3, 4, 3, 5
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OFFSET
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0,1
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COMMENTS
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The counting procedure and "eventually period 6 theorem" are introduced at A225660. Conjecture: if a(n) > 6, then a(n) is odd.
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LINKS
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EXAMPLE
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To see that a(11) = 2, note that 11 = (23 in base 4), and write 23 -> 0011 -> 22 -> 002 -> 201 -> 111 -> 03 -> 1001 -> 22. This shows that the 2 nonrepeating vectors are (2,3) 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.
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MATHEMATICA
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Clear[a, t]; Flatten[Table[a = {t = IntegerDigits[n, 4]};
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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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