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A344259
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For any number n with binary expansion (b(1), ..., b(k)), the binary expansion of a(n) is (b(1), ..., b(ceiling(k/2))).
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2
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0, 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
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OFFSET
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0,5
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COMMENTS
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Leading zeros are ignored.
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LINKS
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FORMULA
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a(n XOR A344220(n)) = a(n) (where XOR denotes the bitwise XOR operator).
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EXAMPLE
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The first terms, alongside their binary expansion, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 1 11 1
4 2 100 10
5 2 101 10
6 3 110 11
7 3 111 11
8 2 1000 10
9 2 1001 10
10 2 1010 10
11 2 1011 10
12 3 1100 11
13 3 1101 11
14 3 1110 11
15 3 1111 11
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MATHEMATICA
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Array[FromDigits[First@Partition[l=IntegerDigits[#, 2], Ceiling[Length@l/2]], 2]&, 100, 0] (* Giorgos Kalogeropoulos, May 14 2021 *)
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PROG
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(PARI) a(n) = n\2^(#binary(n)\2)
(Python)
def a(n): b = bin(n)[2:]; return int(b[:(len(b)+1)//2], 2)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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