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A289194
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Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has no isolated 1 in its base-2 representation.
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1
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1, 3, 2, 6, 4, 7, 8, 12, 5, 11, 9, 14, 16, 15, 13, 19, 21, 22, 10, 23, 17, 24, 18, 27, 29, 30, 26, 35, 52, 38, 25, 31, 32, 28, 33, 47, 34, 46, 20, 39, 40, 44, 36, 43, 37, 48, 41, 75, 53, 59, 61, 54, 57, 55, 58, 60, 64, 51, 65, 56, 66, 62, 50, 71, 45, 78, 42
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OFFSET
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1,2
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COMMENTS
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A144795 gives the numbers without isolated 1's in base-2 representation.
This sequence is conjectured to be a permutation of the natural numbers.
This sequence has similarities with A269361: here we require that the product of two consecutive terms has no isolated 1, there the product of two consecutive terms has only isolated 1's, in base-2 representation.
For any k > 0:
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LINKS
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EXAMPLE
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The first terms, alongside a(n)*a(n+1) in binary, are:
n a(n) a(n)*a(n+1) in binary
-- ---- ---------------------
1 1 11
2 3 110
3 2 1100
4 6 11000
5 4 11100
6 7 111000
7 8 1100000
8 12 111100
9 5 110111
10 11 1100011
11 9 1111110
12 14 11100000
13 16 11110000
14 15 11000011
15 13 11110111
16 19 110001111
17 21 111001110
18 22 11011100
19 10 11100110
20 23 110000111
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MATHEMATICA
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a = {1}; Do[k = 1; While[Nand[! MemberQ[a, k], ! MemberQ[Length /@ DeleteCases[Split[IntegerDigits[k Last[a], 2]], s_ /; First@ s == 0], 1]], k++]; AppendTo[a, k], {n, 2, 67}]; a (* Michael De Vlieger, Jun 29 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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