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A101319
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a(1) = 1; a(n) = (largest odd divisor of a(n-1))th smallest positive integer not yet in the sequence.
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3
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1, 2, 3, 6, 7, 12, 8, 4, 5, 14, 17, 28, 18, 21, 35, 50, 40, 15, 30, 31, 51, 72, 23, 43, 66, 56, 20, 16, 9, 27, 54, 55, 87, 120, 38, 45, 79, 115, 153, 192, 13, 37, 73, 112, 26, 41, 81, 126, 105, 152, 52, 42, 59, 104, 44, 36, 33, 78, 88, 46, 67, 124, 80, 24, 19, 64, 10, 32, 11, 58
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OFFSET
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1,2
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COMMENTS
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It seems likely, but not certain, that this sequence is a permutation of the positive integers, which it is if and only if there are an infinite number of powers of 2 in the sequence.
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LINKS
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EXAMPLE
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a(6) = 12 and the highest odd divisor of 12 is 3. Among the first 6 terms of the sequence is not 4, 5, 8, 9, ... and the 3rd of these is 8, which is therefore a(7).
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MATHEMATICA
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Nest[Append[#, Complement[Range[Max[#] + (r = #[[-1]]/2^IntegerExponent[#[[-1]], 2])], #][[r]]] &, {1}, 69] (* Ivan Neretin, Sep 03 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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