A215136 Start with n, iterate the process x -> x*3-1 until reaching a prime; then a(n) is the number of iterations required, or 0 if no prime is ever reached.

1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 8, 3, 2, 1, 2, 1, 2, 1, 2, 1, 4892, 47, 4, 1, 10, 5, 2, 1, 2, 1, 44, 7, 2, 1, 2, 1, 4, 1, 2, 9, 12, 11, 2, 1, 2, 1, 2, 3, 4, 1, 4, 367, 4, 5, 2, 1, 2, 1, 12, 1, 12, 4891, 2, 1, 46, 1, 2, 3, 2, 3, 4, 3, 2, 9, 6, 1, 4, 1, 4, 1, 4, 27

Offset: 1

Author

Alex Ratushnyak, Aug 04 2012

Keywords

• nonn

Comments

At least one iteration must be made.

Corresponding primes: 2, 5, 23, 11, 41, 17, 59, 23, 6197, 29, 68891, 311, 113, 41, 131, 47, 149, 53, 167, 59, ...

Examples

			n=3: 3 => 8 => 23, so a(3)=2.
n=9: 9 => 26 => 77 => 230 => 689 => 2066 => 6197, so a(9)=6.
		

Crossrefs

Cf. A000040, A078681.

Programs

Java

import java.math.BigInteger;
public class A215136 {
  public static void main (String[] args) {
    long n, t, step;
    BigInteger BI1 = BigInteger.valueOf(1);
    BigInteger BI3 = BigInteger.valueOf(3);
    for (n=1; n<3333; ++n) {
      BigInteger bn = BigInteger.valueOf(n);
      t = n;
      for (step=1; step<9999; ++step) {
        bn = bn.multiply(BI3).subtract(BI1);
        t = (t*3+614889782588491409L) % 614889782588491410L;   // A002110(15)
        if (t<=47 || (t%2>0 && t%3>0 && t%5>0 && t%7>0 && t%11>0 && t%13>0 && t%17>0 && t%19>0 && t%23>0 && t%29>0 && t%31>0 && t%37>0 && t%41>0 && t%43>0 && t%47>0) ) {
          if (bn.isProbablePrime(2)) {
            if (bn.isProbablePrime(80)) break;
          }
        }
      }
      if (step==9999) System.out.printf("---(%d), ", n);
      else            System.out.printf("%d, ", step);
    }
  }
}