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%I #15 Oct 16 2012 14:26:41
%S 1,5,18,46,137,384,1059,2905,8066,21883,59743,162247,441824
%N Last time n appears in the first differences of n*log(n): A217865.
%C Conjecture: the last time n appears is always before the first time n+2 appears.
%C For example, examine: 1, 2, 2, 3, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 4, 3, 4, 4, 5, 4, 4, 4 (A217865).
%C We can see that the last 2 is before the first 4, the last 3 is before the first 5, etc.
%e 2 lasts appears in A217865 at position 5 so a(2)=5.
%o (JavaScript)
%o function lastIndex(arr,k) {
%o p=-1;
%o for (a=1;a<arr.length;a++) if (arr[a]==k) p=a;
%o return p;
%o }
%o d=new Array();
%o for (i=1;i<500000;i++)
%o d[i]=Math.floor((i+1)*Math.log(i+1))-Math.floor(i*Math.log(i));
%o for (i=1;i<100;i++) document.write(lastIndex(d,i)+", ");
%Y Cf. A217865.
%Y Cf. A217976.
%K nonn
%O 1,2
%A _Jon Perry_, Oct 13 2012
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