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

1,4

Comments

At each step, the minimum available integer is used.

Links

Table of n, a(n) for n=1..74.

Example

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.

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);

Crossrefs

Cf. A018252, A181642.

Sequence in context: A284282 A132774 A294721 * A007945 A011150 A100112

Adjacent sequences: A300813 A300814 A300815 * A300817 A300818 A300819

Keyword

nonn,easy

Author

Paolo P. Lava, Mar 13 2018

Status

approved