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Topic: binary (Read 870 times) |
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mad
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Let f(k) = y where k is the y-th number in the increasing sequence of non-negative integers with the same number of ones in its binary representation as y, e.g. f(0) = 1, f(1) = 1, f(2) = 2, f(3) = 1, f(4) = 3, f(5) = 2, f(6) = 3 and so on. Given k >= 0, compute f(k).
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towr
wu::riddles Moderator
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Re: binary
« Reply #1 on: Jul 31st, 2007, 2:26pm » |
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I can't entirely understand the way you've phrased that..
Is f(k) an inverse function, because it seems k depends on y rather than vice versa.
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Eigenray
wu::riddles Moderator
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Re: binary
« Reply #2 on: Jul 31st, 2007, 2:55pm » |
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It's basically the "prime bits" problem. Except not necessarily prime.
(Inverse problem here and here.)
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| « Last Edit: Jul 31st, 2007, 2:57pm by Eigenray » |
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towr
wu::riddles Moderator
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Re: binary
« Reply #3 on: Jul 31st, 2007, 3:03pm » |
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Ah, f(k) is the count of nonnegative numbers  k with the same number of bits set to one as k.
Now I understand it.
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| « Last Edit: Jul 31st, 2007, 3:04pm by towr » |
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mad
Junior Member
Posts: 118
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Re: binary
« Reply #4 on: Jul 31st, 2007, 3:31pm » |
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Eg.
1010
will come after
0011
0101
0110
1001
1010
So, it is the 5th number here.
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