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A343852
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a(n) is the least k > 0 such that the binary expansions of k and of n + k have the same numbers of 0's and of 1's.
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2
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5, 10, 9, 20, 21, 18, 17, 40, 19, 42, 38, 36, 37, 34, 33, 80, 35, 38, 37, 84, 35, 76, 74, 72, 73, 74, 70, 68, 69, 66, 65, 160, 67, 70, 69, 76, 67, 74, 73, 168, 75, 70, 69, 152, 67, 148, 146, 144, 71, 146, 145, 148, 140, 140, 138, 136, 137, 138, 134, 132, 133
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OFFSET
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1,1
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COMMENTS
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This is the binary analog of A343888.
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LINKS
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FORMULA
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EXAMPLE
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The first terms, alongside the binary expansions of a(n) and of n + a(n), are:
n a(n) bin(a(n)) bin(n+a(n))
-- ---- --------- -----------
1 5 101 110
2 10 1010 1100
3 9 1001 1100
4 20 10100 11000
5 21 10101 11010
6 18 10010 11000
7 17 10001 11000
8 40 101000 110000
9 19 10011 11100
10 42 101010 110100
11 38 100110 110001
12 36 100100 110000
13 37 100101 110010
14 34 100010 110000
15 33 100001 110000
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PROG
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(PARI) a(n) = { for (k=1, oo, if (#binary(k)==#binary(n+k) && hammingweight(k)==hammingweight(n+k), return (k))) }
(Python)
def a(n):
k = 1
while k.bit_length() != (n+k).bit_length() or bin(k).count('1') != bin(n+k).count('1'): k += 1
return k
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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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