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%I #36 Jan 15 2015 10:18:49
%S 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,
%T 55,26,33,28,45,32,51,38,17,19,30,119,36,65,34,57,40,63,44,69,50,23,
%U 42,85,46,75,52,81,56,87,62,29,31,48
%N 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).
%C The sequence differs from A098550 from a(11) onward.
%C 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
%H Robert Israel, <a href="/A247942/b247942.txt">Table of n, a(n) for n = 1..10000</a>
%H David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669, 2015.
%p for n from 1 to 3 do
%p a[n]:= n:
%p b[n]:= 1:
%p od:
%p for n from 4 to 1000 do
%p q:= a[n-2]*a[n-3];
%p for k from 4 do
%p if not assigned(b[k]) and igcd(k,q) > 1 and igcd(k,a[n-1]) = 1 then
%p a[n]:= k;
%p b[k]:= 1;
%p break
%p fi
%p od:
%p od:
%p seq(a[i],i=1..1000); # _Robert Israel_, Jan 12 2015
%t 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 *)
%Y Cf. A098550, A249167, A251604, A247225.
%K nonn
%O 1,2
%A _Vladimir Shevelev_, Jan 11 2015
%E More terms from _Jean-François Alcover_, Jan 12 2015
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