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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..68.

Example

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.

Prog

(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}

Crossrefs

Cf. A072009, A065187, A167048, A167047

Sequence in context: A010777 A336050 A103887 * A283745 A341813 A088446

Adjacent sequences: A167043 A167044 A167045 * A167047 A167048 A167049

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 27 2009

Status

approved