A167046 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.
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, 52, 55, 58, 12, 20, 61, 64, 67, 23, 70, 15, 73, 76, 26, 79, 82, 85, 18, 29, 88, 91, 32, 94, 97, 100, 103, 21, 35, 106, 109, 112, 38, 115, 24, 118, 41, 121, 124, 127, 130, 133, 27
Offset: 1
Keywords
Examples
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.
Programs
-
PARI
dist(n) = n+1 al(n) = {local(d,v,w,mn,j); v=vector(n);w=vector(n); v[1]=w[1]=1;mn=2; for(k=2,n, d=dist(k); if(w[k-1]-d>=mn, j=mn;mn++;while(v[mn],mn++), j=w[k-1]+d;while(j<=#v&v[j],j++);if(j>#v,v=vector(j,i,if(i<=#v,v[i],0)))); v[j]=k;w[k]=j); v}
Comments