A167046 - OEIS

%I #2 Mar 30 2012 17:35:24

%S 1,4,7,2,10,13,16,3,5,19,22,8,25,28,31,6,11,34,37,40,14,9,43,46,17,49,

%T 52,55,58,12,20,61,64,67,23,70,15,73,76,26,79,82,85,18,29,88,91,32,94,

%U 97,100,103,21,35,106,109,112,38,115,24,118,41,121,124,127,130,133,27

%N Angry numbers: each number n must be more than n places from n-1 and n+1. This sequence places each number as early as possible.

%C This sequence is a permutation of the positive integers. After any two increases in the position of n from after the first hole, it will be possible to put the next number in that hole.

%e For a(n) = 2, n must be at least 3 away from a^{-1}(1) = 1, so n = 4. Next, a(n) = 3 must be 4 away from 4, so it can't be less than 4; hence a(8) = 3. Then a(n) = 4 must be 5 away from 8; the first hole at 2 is far enough, so a(2) = 4.

%o (PARI) dist(n) = n+1

%o al(n) = {local(d,v,w,mn,j);

%o v=vector(n);w=vector(n);

%o v[1]=w[1]=1;mn=2;

%o for(k=2,n,

%o d=dist(k);

%o if(w[k-1]-d>=mn,

%o j=mn;mn++;while(v[mn],mn++),

%o j=w[k-1]+d;while(j<=#v&v[j],j++);if(j>#v,v=vector(j,i,if(i<=#v,v[i],0))));

%o v[j]=k;w[k]=j);

%o v}

%Y Cf. A072009, A065187, A167048, A167047

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Oct 27 2009