A234799 - OEIS

%I #6 Jan 02 2014 06:19:32

%S 11,13,47,83,193,199,223,227,263,269,439,571,887,911,929,1013,1019,

%T 1031,1151,1163,1571,1597,1619,1723,1733,1741,1747,1759,1787,1801,

%U 1907,2503,2707,2741,3803,3833,3863,4337,4373,4409,5479,5483,5519,5779,5813,5843,5849,6011

%N Primes p such that abs(p-s) and abs(p-c) are primes, where s is the square nearest to p, and c is the nearest to p cube, c!=s.

%e 11 is in the sequence because distances to the nearest square and cube (9 and 8) are prime numbers.

%o (Java)

%o import java.math.*;

%o public class A234799 {

%o   public static void main (String[] args) {

%o     for (long k = 1; ; k++)

%o       if (BigInteger.valueOf(k).isProbablePrime(50)) {

%o         long r2 = (long)Math.sqrt(k);

%o         if (r2*r2==k) continue;

%o         long r3 = (long)Math.cbrt(k);

%o         if (r3*r3*r3==k) continue;

%o         long b2 = r2*r2,    a2 = (r2+1)*(r2+1);

%o         long b3 = r3*r3*r3, a3 = (r3+1)*(r3+1)*(r3+1);

%o         long s = (k-b2<=a2-k)? b2 : a2;

%o         long c = (k-b3<=a3-k)? b3 : a3;

%o         long nrst2 = Math.abs(s-k);

%o         long nrst3 = Math.abs(c-k);

%o         if (s!=c &&

%o           BigInteger.valueOf(nrst2).isProbablePrime(50) &&

%o           BigInteger.valueOf(nrst3).isProbablePrime(50))

%o             System.out.printf("%d, ", k);

%o       }

%o   }

%o }

%Y Cf. A000040.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Dec 30 2013