A234798 Numbers k such that (k^i)+7 for 1<=i<=7 are seven prime numbers.

0, 3981186, 146202480, 1165139284, 2002776304, 5677052574, 9441118506, 13199287564, 14655461200, 21663769144, 23911959136, 28132616434, 29959257966, 34716681516, 35619315204, 35690387094, 38966503234, 42887165056, 45425679640, 47063988520, 51444908350, 53558122980

Offset

1,2

Comments

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..22.

Example

0 is in the sequence since (0^i)+7 = 7 is prime for i>0.
3981186 is in the sequence because the following seven numbers are primes: 3981186+7, 3981186^2+7, ..., 3981186^7+7.

Prog

(Java)
import java.math.*;
public class A234798 {
public static void main (String[] args) {
  BigInteger c7 = BigInteger.valueOf(7);
  for (long i=0; ; i+=2) {
    if (!BigInteger.valueOf(i+7).isProbablePrime(80))
      continue;
    BigInteger bi = BigInteger.valueOf(i), b=bi;
    long k;
    for (k=1; k<7; ++k) {
      b = b.multiply(bi);
      if (!b.add(c7).isProbablePrime(80)) break;
    }
    if (k==7)  System.out.printf("%d, ", i);
  }
}
}

Crossrefs

Cf. A000040.

Sequence in context: A144642 A032753 A047987 * A290123 A146946 A109207

Adjacent sequences: A234795 A234796 A234797 * A234799 A234800 A234801

Keyword

nonn,hard

Author

Alex Ratushnyak, Dec 30 2013

Status

approved