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%I #2 Mar 30 2012 17:35:24
%S 1,3,5,7,9,2,11,13,4,15,17,6,19,21,8,23,25,27,10,29,31,12,33,35,37,14,
%T 39,41,16,43,45,47,18,49,51,20,53,55,57,22,59,61,24,63,65,26,67,69,71,
%U 28,73,75,30,77,79,81,32,83,85,34,87,89,36,91,93,95,38,97,99,40,101,103
%N Angry numbers: each number n must be more than n places from n-1 and n+1. This sequence makes each number as small as possible as it occurs.
%C This sequence is a permutation of the positive integers. A number cannot remain unassigned indefinitely; eventually the placement gets far enough from its neighbors and it gets used.
%C Each term in this sequence is either the next unused even number or the next unused odd number; after the initial 5 terms there are always 2 or 3 odd numbers between each pair of even numbers.
%e After a(1) = 1, we cannot have a(2) = 2, because then 1 and 2 would be too close. a(2) = 3 is OK. Now a(3) can't be 2 because then 2 and 3 would be too close; 4 would also be too close to 3, but 5 is OK. Skipping ahead, a(6) is the first place where 2 is not too close to 3, so a(6) = 2.
%o (PARI) dist(n) = n+1
%o al(n)= {local(v,w,mn,ok);
%o v=vector(n);w=vector(2*n);u=vector(n);
%o v[1]=w[1]=1;mn=2;
%o for(k=2,n,
%o j=mn-1;ok=0;
%o while(!ok,
%o j++;ok=w[j]==0;
%o if(ok&w[j-1]&abs(k-w[j-1])<dist(j),ok=0);
%o if(ok&w[j+1]&abs(k-w[j+1])<dist(j+1),ok=0));
%o v[k]=j;w[j]=k);
%o while(w[mn],mn++);
%o v}
%Y Cf. A167046, A167049.
%K nonn
%O 1,2
%A _Franklin T. Adams-Watters_, Oct 27 2009
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