A231979 Numbers n such that for every digit d in n, 2*n + 6*d - 3 is prime.

1, 2, 4, 5, 7, 8, 10, 13, 17, 19, 22, 29, 32, 34, 37, 43, 44, 50, 52, 55, 65, 67, 70, 77, 83, 89, 112, 113, 115, 118, 124, 127, 133, 145, 152, 155, 167, 172, 182, 188, 199, 200, 215, 229, 274, 277, 295, 302, 308, 322, 362, 379, 400, 418, 433, 488, 494, 499

Offset: 1

Author

John R Phelan, Nov 16 2013

Keywords

• nonn
• easy
• base

Comments

The coefficients 2,6,-3 yield more hits between 1 and 1000000 than 2,2,1 or 1,1,1.

Examples

			124 is in the sequence since
  2*124+6*1-3=251 which is prime,
  2*124+6*2-3=257 which is prime,
  2*124+6*4-3=269 which is prime.
241 is NOT in the sequence since
  2*241+6*2-3=491 which is prime,
  2*241+6*4-3=503 which is prime,
  but 2*241+6*1-3=485 which is not prime.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..2000

Programs

Java

public class Ndp {
// 2n+6d-3 is prime for all digits d in n
private static final int MAX = 1000000;
public static void main(String[] args) {
  String sequence = "";
  loop: for (int n = 1; sequence.length() < 250 && n < MAX; n++) {
   for (int i = n; i > 0; i /= 10) {
    int d = i % 10;
    if (!isPrime(2 * n + 6 * d - 3)) {
     continue loop;
    }
   }
   sequence += n + ",";
  }
  System.out.println(sequence);
}
private static boolean isPrime(long n) {
  for (long i = 2; i <= Math.sqrt(n); i++) {
   if (n < 2 || n % i == 0) {
    return false;
   }
  }
  return true;
}
}

Mathematica

fQ[n_] := Module[{d = IntegerDigits[n]}, And @@ PrimeQ[2*n + 6*d - 3]]; Select[Range[1000], fQ] (* T. D. Noe, Nov 19 2013 *)