A234799 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.

11, 13, 47, 83, 193, 199, 223, 227, 263, 269, 439, 571, 887, 911, 929, 1013, 1019, 1031, 1151, 1163, 1571, 1597, 1619, 1723, 1733, 1741, 1747, 1759, 1787, 1801, 1907, 2503, 2707, 2741, 3803, 3833, 3863, 4337, 4373, 4409, 5479, 5483, 5519, 5779, 5813, 5843, 5849, 6011

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Example

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

Prog

(Java)
import java.math.*;
public class A234799 {
  public static void main (String[] args) {
    for (long k = 1; ; k++)
      if (BigInteger.valueOf(k).isProbablePrime(50)) {
        long r2 = (long)Math.sqrt(k);
        if (r2*r2==k) continue;
        long r3 = (long)Math.cbrt(k);
        if (r3*r3*r3==k) continue;
        long b2 = r2*r2,    a2 = (r2+1)*(r2+1);
        long b3 = r3*r3*r3, a3 = (r3+1)*(r3+1)*(r3+1);
        long s = (k-b2<=a2-k)? b2 : a2;
        long c = (k-b3<=a3-k)? b3 : a3;
        long nrst2 = Math.abs(s-k);
        long nrst3 = Math.abs(c-k);
        if (s!=c &&
          BigInteger.valueOf(nrst2).isProbablePrime(50) &&
          BigInteger.valueOf(nrst3).isProbablePrime(50))
            System.out.printf("%d, ", k);
      }
  }
}

Crossrefs

Cf. A000040.

Sequence in context: A154292 A188386 A027450 * A036295 A132201 A057189

Adjacent sequences: A234796 A234797 A234798 * A234800 A234801 A234802

Keyword

nonn

Author

Alex Ratushnyak, Dec 30 2013

Status

approved