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A257405
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For n=1 or prime, a(n)=n; otherwise, a(n) is the smallest number not already used which shares a factor with a(n-1).
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2
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1, 2, 3, 6, 5, 10, 7, 14, 4, 8, 11, 22, 13, 26, 12, 9, 17, 34, 19, 38, 16, 18, 23, 46, 20, 15, 21, 24, 29, 58, 31, 62, 28, 30, 25, 35, 37, 74, 32, 36, 41, 82, 43, 86, 40, 42, 47, 94, 44, 33, 27, 39, 53, 106, 48, 45, 50, 52, 59, 118, 61, 122, 54, 51, 57, 60, 67
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OFFSET
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1,2
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COMMENTS
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Since limsup(prime(n)) is infinity, it is easy to see that the sequence contains all even numbers. So it is natural to conjecture that the sequence is a permutation of the positive integers.
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LINKS
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MATHEMATICA
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seq={1}; Do[cmplSeq=Complement[Range[2*Max[seq]], seq];
If[PrimeQ[n], AppendTo[seq, n], AppendTo[seq, Min[Select[cmplSeq, GCD[Last[seq], #]>1&]]]], {n, 2, 100}]; seq (* Ivan N. Ianakiev, Apr 25 2015 *)
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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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