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A225665
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Number of nonrepeating vectors in a counting procedure that starts with the digits of (n base 16).
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7
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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
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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) is odd for only finitely many n.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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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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