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A306378
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Number of steps of applying "Erase or triple" protocol to n before reaching 0, 5, 7, or 89.
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0
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0, 16, 10, 15, 10, 0, 9, 0, 9, 14, 22, 1, 9, 3, 24, 8, 19, 8, 8, 3, 10, 11, 1, 6, 8, 3, 22, 13, 3, 16, 21, 8, 13, 1, 19, 21, 8, 2, 12, 2, 12, 4, 23, 13, 1, 7, 19, 12, 18, 19, 12, 7, 26, 13, 7, 1, 30, 2, 3, 18, 9, 18, 12, 10, 15, 12, 1, 32, 14, 5, 6, 21, 7, 21
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OFFSET
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0,2
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COMMENTS
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The "Erase or triple" protocol is described in A300148 and each trajectory converges to one of 4 loops. Since for n > 9876543210, this protocol take n to a number <= 876543210, it suffices to only look at the trajectories of n under this protocal for 0 <= n <= 9876543210.
a(n) <= 52 for all n. For n <= 9876543210, a(n) is maximal at a(n) = 52 for 994 different numbers, the smallest of which is 445016392 and the largest of which is 9849720163 and all these trajectories converge to 0. Each of these 994 numbers either has nonunique digits or is pandigital, and thus cannot be the result of an "erase" operation, i.e. cannot be part of trajectory that started larger than 9876543210, thus for n > 9876543210, a(n) <= 51 + 1 = 52.
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LINKS
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EXAMPLE
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The trajectory of 2 is 2, 6, 18, 54, 162, 486, 1458, 4374, 37, 111, 0, 0, ...
The trajectory of 10 is 10, 30, 90, 270, 810, 2430, 7290, 21870, 65610, 510, 1530, 4590, 13770, 130, 390, 1170, 70, 210, 630, 1890, 5670, 17010, 7, ...
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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