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A247942
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a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common factor with a(n-2)*a(n-3), but none with a(n-1).
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8
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1, 2, 3, 4, 9, 8, 15, 14, 5, 6, 7, 10, 21, 16, 25, 12, 35, 18, 49, 20, 27, 22, 39, 11, 13, 24, 55, 26, 33, 28, 45, 32, 51, 38, 17, 19, 30, 119, 36, 65, 34, 57, 40, 63, 44, 69, 50, 23, 42, 85, 46, 75, 52, 81, 56, 87, 62, 29, 31, 48
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OFFSET
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1,2
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COMMENTS
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The sequence differs from A098550 from a(11) onward.
The sequence is a permutation of the natural numbers. The proof is similar to that for A098550 (with minor changes). - Vladimir Shevelev, Jan 14 2015
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LINKS
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David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015.
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MAPLE
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for n from 1 to 3 do
a[n]:= n:
b[n]:= 1:
od:
for n from 4 to 1000 do
q:= a[n-2]*a[n-3];
for k from 4 do
if not assigned(b[k]) and igcd(k, q) > 1 and igcd(k, a[n-1]) = 1 then
a[n]:= k;
b[k]:= 1;
break
fi
od:
od:
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MATHEMATICA
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a[n_ /; n <= 3] := n; a[n_] := a[n] = For[aa = Table[a[j], {j, 1, n-1}]; k=4, True, k++, If[FreeQ[aa, k] && !CoprimeQ[k, a[n-2]*a[n-3]] && CoprimeQ[k, a[n-1]], Return[k]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jan 12 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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