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A352809
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Lexicographically earliest sequence of distinct nonnegative integers such that for any proper divisor d of n the binary expansions of a(d) and a(n) have no common 1's.
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3
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0, 1, 2, 4, 3, 8, 5, 10, 9, 12, 6, 16, 7, 18, 20, 32, 11, 36, 13, 48, 24, 40, 14, 64, 28, 56, 52, 72, 15, 96, 17, 80, 25, 68, 88, 128, 19, 34, 104, 192, 21, 160, 22, 144, 224, 112, 23, 256, 26, 288, 84, 320, 27, 384, 120, 416, 176, 208, 29, 512, 30, 38, 352
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OFFSET
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1,3
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COMMENTS
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This sequence is a bijection from the positive integers onto the nonnegative integers (with inverse A353266); as a(1) = 0, for any prime number p, a(p) is the least value not yet in the sequence, and eventually every nonnegative integer will appear in the sequence.
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LINKS
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EXAMPLE
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The first terms, alongside their binary expansion, proper divisors and implied forbidden bits, are:
n a(n) bin(a(n)) proper divisors bin(forbidden)
-- ---- ------ --------------- --------------
1 0 0 {} 0
2 1 1 {1} 0
3 2 10 {1} 0
4 4 100 {1, 2} 1
5 3 11 {1} 0
6 8 1000 {1, 2, 3} 11
7 5 101 {1} 0
8 10 1010 {1, 2, 3} 101
9 9 1001 {1, 2} 10
10 12 1100 {1, 2, 3} 11
11 6 110 {1} 0
12 16 10000 {1, 2, 3, 4, 5} 1111
13 7 111 {1} 0
14 18 10010 {1, 2, 3} 101
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PROG
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(PARI) 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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