A216266 Number of primes between n^3 and n^3+n (inclusive).

1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 2, 2, 1, 2, 1, 3, 3, 3, 2, 4, 0, 3, 5, 4, 4, 2, 3, 2, 2, 5, 3, 3, 2, 5, 2, 3, 4, 5, 2, 3, 3, 5, 8, 5, 4, 5, 4, 3, 6, 6, 4, 4, 6, 5, 3, 7, 8, 2, 3, 6, 6, 5, 4, 5, 6, 5, 4, 4, 3, 4, 8, 8, 4, 5, 8, 7, 6, 5, 4, 5, 9, 6, 8, 8, 6, 8, 10, 6, 9, 11

Offset

1,7

Comments

Conjecture: a(n)>0 for n>23.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000720(n^3+n) - A000720(n^3).

Maple

a:= n-> add(`if`(isprime(t), 1, 0), t=n^3..n^3+n):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 17 2013

Mathematica

Table[PrimePi[n^3+n]-PrimePi[n^3], {n, 100}] (* Harvey P. Dale, Apr 19 2014 *)

Prog

(Java)
import java.math.BigInteger;
public class A216266 {
    public static void main (String[] args) {
      for (long n=1; n < (1<<21); n++) {
        long cube = n*n*n, c = 0;
        for (long k=cube+1; k<=cube+n; ++k) {
          BigInteger b1 = BigInteger.valueOf(k);
          if (b1.isProbablePrime(2)) {
            if (b1.isProbablePrime(80))
              ++c;
          }
        }
        System.out.printf("%d, ", c);
      }
    }
}
(PARI)
default(primelimit, 10^7);
a(n) = primepi(n^3+n) - primepi(n^3);
/* Joerg Arndt, Mar 16 2013 */

Crossrefs

Cf. A089610, A216265.

Sequence in context: A332038 A101672 A083731 * A177416 A087606 A271368

Adjacent sequences: A216263 A216264 A216265 * A216267 A216268 A216269

Keyword

nonn

Author

Alex Ratushnyak, Mar 15 2013

Status

approved