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A216266 Number of primes between n^3 and n^3+n (inclusive). 4
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 (list; graph; refs; listen; history; text; internal format)
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: A204688 A101672 A083731 * A177416 A087606 A271368

Adjacent sequences:  A216263 A216264 A216265 * A216267 A216268 A216269

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Mar 15 2013

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)