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A216265 Number of primes between n^3 - n and n^3. 3
0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 0, 2, 3, 2, 2, 2, 2, 1, 2, 3, 4, 1, 3, 3, 2, 3, 3, 3, 2, 1, 3, 2, 4, 4, 3, 2, 1, 2, 7, 4, 2, 2, 4, 3, 4, 7, 3, 5, 7, 4, 6, 5, 4, 2, 8, 4, 3, 4, 2, 5, 7, 7, 4, 3, 8, 4, 1, 3, 2, 10, 4, 5, 4, 6, 7, 8, 6, 6, 1, 6, 8, 8, 7, 7, 6, 7, 4, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Conjecture: a(n) > 0 for n > 13.

LINKS

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

FORMULA

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

EXAMPLE

a(9) = 1 because between 9^3 - 9 and 9^3 there is just one prime (727).

a(10) = 2 because between 10^3 - 10 and 10^3 there are two primes (991 and 997).

a(11) = 2 because between 11^3 - 11 and 11^3 there are two primes (1321 and 1327).

MAPLE

a:= n-> add(`if`(isprime(t), 1, 0), t=n^3-n..n^3):

seq(a(n), n=1..100);  # Alois P. Heinz, Mar 17 2013

MATHEMATICA

Table[PrimePi[n^3] - PrimePi[n^3 - n], {n, 100}] (* Alonso del Arte, Mar 17 2013 *)

PROG

(Java)

import java.math.BigInteger;

public class A216265 {

    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 - n; k < cube; ++k) {

          BigInteger b1 = BigInteger.valueOf(k);

          if (b1.isProbablePrime(2)) {

            if (b1.isProbablePrime(80))

              ++c;

          }

        }

        System.out.printf("%d, ", c);

      }

    }

} // Ratushnyak

(PARI)

default(primelimit, 10^7);

a(n) = primepi(n^3) - primepi(n^3-n);

/* Joerg Arndt, Mar 16 2013 */

CROSSREFS

Cf. A094189, A216266.

Sequence in context: A223175 A322213 A118205 * A130277 A109135 A264136

Adjacent sequences:  A216262 A216263 A216264 * A216266 A216267 A216268

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Mar 15 2013

STATUS

approved

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Last modified July 18 21:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)