A181642 Minimal sequence whose forwards van Eck transform is the sequence of prime numbers.

0, 1, 0, 2, 1, 3, 4, 0, 5, 6, 2, 7, 8, 9, 10, 1, 11, 12, 3, 13, 14, 15, 16, 4, 17, 18, 0, 19, 20, 21, 22, 5, 23, 24, 25, 26, 27, 28, 6, 29, 30, 2, 31, 32, 33, 34, 35, 36, 7, 37, 38, 39, 40, 8, 41, 42, 9, 43, 44, 45, 46, 10, 47, 48, 49, 50, 51, 52, 1, 53, 54

Offset

1,4

Comments

At each step, the minimum available integer is used.

From Rémy Sigrist, Aug 12 2017: (Start)

a(n)=0 iff n belongs to A074271.

a(n)=1 iff n > 1 and n belongs to A259408.

For any k > 0, A064427(k) = least n such that a(n) = k-1.

(End)

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Example

a(1)=0. Next 0 is at distance 2 (1st prime): a(3)=0.
a(2)=1. Next 1 is at distance 3 (2nd prime): a(5)=1.
a(3)=0. Next 0 is at distance 5 (3rd prime): a(8)=0.
For a(4), we can use neither 0 (distance 1 from previous 0 would lead to an incongruence) nor 1 (distance 1 from subsequent 1 would lead to another incongruence). Therefore we must use 2.
Next 2 must be at distance 7 (4th prime): a(11)=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 isprime(n) then  i:=i+1; if x[i]>-1 then x[i+n]:=x[i]; else t:=t+1; x[i]:=t; x[i+n]:=x[i]; fi; fi; od; seq(x[k], k=1..79); end: P(400, 500);

Prog

(PARI) a = vector(71, i, -1); u = 0; for (n=1, #a, if (a[n]<0, o = n; while (o <= #a, a[o] = u; o += prime(o)); u++); print1 (a[n] ", ")) \\ Rémy Sigrist, Aug 12 2017

Crossrefs

Cf. A000040, A064427, A074271, A181391, A259408.

Sequence in context: A061413 A286385 A074743 * A011358 A160188 A332864

Adjacent sequences: A181639 A181640 A181641 * A181643 A181644 A181645

Keyword

easy,nonn

Author

Paolo P. Lava & Giorgio Balzarotti, Nov 03 2010

Extensions

More terms from Rémy Sigrist, Aug 12 2017

Status

approved