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A367262
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Lexicographically earliest sequence of distinct nonnegative integers such that the values a(0) XOR ... XOR a(k) (for some k >= 0) are all distinct (where XOR denotes the bitwise XOR operator).
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3
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0, 1, 2, 4, 3, 6, 7, 8, 5, 14, 9, 16, 10, 11, 12, 15, 13, 25, 17, 18, 19, 21, 22, 20, 24, 29, 23, 32, 26, 27, 28, 30, 31, 49, 33, 35, 34, 37, 38, 41, 40, 36, 44, 64, 39, 42, 43, 45, 46, 47, 48, 50, 51, 52, 54, 53, 56, 55, 59, 57, 60, 58, 66, 65, 69, 67, 61, 96
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OFFSET
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0,3
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COMMENTS
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This sequence is a variant of A333400; here we combine initial terms with the XOR operator, there with the addition.
This sequence is well defined; after some initial terms we can extend the sequence with a power of 2 greater that any prior term or even a smaller value.
This sequence is a permutation of the nonnegative integers (with inverse A367263):
- for any k >= 0, the least value >= 2^k is precisely 2^k,
- all powers of 2 appear in the sequence,
- after a power of 2, if the least value not yet in the sequence is less than this power of 2, then this value will be the next term.
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LINKS
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EXAMPLE
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The first terms are:
n a(n) a(0) XOR ... XOR a(n)
-- ---- ---------------------
0 0 0
1 1 1
2 2 3
3 4 7
4 3 4
5 6 2
6 7 5
7 8 13
8 5 8
9 14 6
10 9 15
11 16 31
12 10 21
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PROG
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(C++) See Links section.
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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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