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A372143
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Lexicographically earliest sequence of distinct nonnegative integers such that for any n > 0, the binary expansions of a(n), a(2*n) and a(2*n+1) have a common 1 bit.
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4
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0, 1, 3, 5, 2, 6, 4, 7, 10, 11, 12, 13, 14, 15, 9, 17, 8, 24, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 16, 31, 40, 41, 42, 43, 34, 35, 33, 37, 36, 38, 39, 44, 45, 46, 47, 49, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 32, 96, 67, 69
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OFFSET
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0,3
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COMMENTS
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Conjecture: this sequence is a permutation of the nonnegative integers.
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LINKS
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FORMULA
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a(n) AND a(2*n) AND a(2*n+1) <> 0 for any n > 0 (where AND denotes the bitwise AND operator).
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EXAMPLE
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The first terms, arranged alongside a binary tree where each parent node (except the root) and its children share some 1 bit, are:
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0
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.-------1-------.
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.---3---. .---5---.
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.-2-. .-6-. .-4-. .-7-.
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10 11 12 13 14 15 9 17
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PROG
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(PARI) \\ See Links section.
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CROSSREFS
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Cf. A372129 (analog without common 1 bit).
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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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