A300816 Minimal sequence whose forwards van Eck transform is the sequence of nonprime numbers.

0, 0, 1, 2, 3, 0, 4, 5, 1, 6, 7, 2, 8, 3, 9, 0, 10, 11, 4, 12, 13, 5, 14, 1, 15, 6, 16, 17, 7, 18, 19, 2, 20, 8, 21, 3, 22, 23, 9, 24, 0, 25, 10, 26, 11, 27, 4, 28, 29, 12, 30, 31, 13, 32, 5, 33, 14, 34, 1, 35, 15, 36, 37, 6, 38, 16, 39, 17, 40, 41, 7, 42, 43, 18

Offset: 1

Author

Paolo P. Lava, Mar 13 2018

Keywords

• nonn
• easy

Comments

At each step, the minimum available integer is used.

Examples

			a(1) = 0. Next 0 is at distance 1: a(2) = 0.
a(2) = 0. Next 0 is at distance 4: a(6) = 0.
For a(3) we cannot use 0 because the next 0 is at distance 3 that is a prime.
Therefore we must use 1: a(3) = 1.
Next 1 must be at distance 6, next composite after 4: a(9) = 1.
Again, for a(4) we cannot use neither 0 nor 1: a(4) = 2.
Next 2 must be at distance 8: a(12) = 2. And so on.
		

Crossrefs

Cf. A018252, A181642.

Programs

Maple

P:=proc(q,h) local i,k,n,t,x; x:=array(1..h);
for k from 1 to h do x[k]:=-1; od; x[1]:=0; i:=0; t:=0;
for n from 1 to q do if not isprime(n) then i:=i+1;
if x[i]=-1 then t:=t+1; x[i]:=t; fi; x[i+n]:=x[i];
fi; od; seq(x[k],k=1..124); end: P(160,300);