A167047 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.

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, 39, 41, 16, 43, 45, 47, 18, 49, 51, 20, 53, 55, 57, 22, 59, 61, 24, 63, 65, 26, 67, 69, 71, 28, 73, 75, 30, 77, 79, 81, 32, 83, 85, 34, 87, 89, 36, 91, 93, 95, 38, 97, 99, 40, 101, 103

Offset

1,2

Comments

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.

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.

Links

Table of n, a(n) for n=1..72.

Example

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.

Prog

(PARI) dist(n) = n+1
al(n)= {local(v, w, mn, ok);
v=vector(n); w=vector(2*n); u=vector(n);
v[1]=w[1]=1; mn=2;
for(k=2, n,
j=mn-1; ok=0;
while(!ok,
j++; ok=w[j]==0;
if(ok&w[j-1]&abs(k-w[j-1])<dist(j), ok=0);
if(ok&w[j+1]&abs(k-w[j+1])<dist(j+1), ok=0));
v[k]=j; w[j]=k);
while(w[mn], mn++);
v}

Crossrefs

Cf. A167046, A167049.

Sequence in context: A131669 A004155 A163125 * A065271 A213542 A029657

Adjacent sequences: A167044 A167045 A167046 * A167048 A167049 A167050

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 27 2009

Status

approved