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A047988
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Start with n and reach 2 by repeatedly either dividing by d where d <= the square root or by adding or subtracting 1. The division steps are free, but adding or subtracting 1 costs 1 point. a(n) is the smallest cost to reach 2.
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17
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0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2
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OFFSET
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2,18
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LINKS
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EXAMPLE
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For n = 19 we get to 2 via
n := 19 - 1 = 2 (+1 point as we subtract 1 from n)
n := 18/3 = 6 (+0 point as we divide by a divisor)
n := 6/2 = 3 (+0 point, we divide by a divisor. we can't divide by 3 as 3 > sqrt(6)).
n := 3 - 1 = 2 (+1 point; steps end here; we have n = 2)
We earned 2 points in these steps. As this is the minimal number of points starting at n = 19, a(19) = 2. (End)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Thomas Kantke (bytes.more(AT)ibm.net)
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EXTENSIONS
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STATUS
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approved
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