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%I #17 Apr 19 2014 08:47:33
%S 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,
%T 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,
%U 4,4,3,4,8,8,4,5,8,7,6,5,4,5,9,6,8,8,6,8,10,6,9,11
%N Number of primes between n^3 and n^3+n (inclusive).
%C Conjecture: a(n)>0 for n>23.
%H Alois P. Heinz, <a href="/A216266/b216266.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000720(n^3+n) - A000720(n^3).
%p a:= n-> add(`if`(isprime(t), 1, 0), t=n^3..n^3+n):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 17 2013
%t Table[PrimePi[n^3+n]-PrimePi[n^3],{n,100}] (* _Harvey P. Dale_, Apr 19 2014 *)
%o (Java)
%o import java.math.BigInteger;
%o public class A216266 {
%o public static void main (String[] args) {
%o for (long n=1; n < (1<<21); n++) {
%o long cube = n*n*n, c = 0;
%o for (long k=cube+1; k<=cube+n; ++k) {
%o BigInteger b1 = BigInteger.valueOf(k);
%o if (b1.isProbablePrime(2)) {
%o if (b1.isProbablePrime(80))
%o ++c;
%o }
%o }
%o System.out.printf("%d, ", c);
%o }
%o }
%o }
%o (PARI)
%o default(primelimit,10^7);
%o a(n) = primepi(n^3+n) - primepi(n^3);
%o /* _Joerg Arndt_, Mar 16 2013 */
%Y Cf. A089610, A216265.
%K nonn
%O 1,7
%A _Alex Ratushnyak_, Mar 15 2013
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