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%I A215136 #10 Aug 05 2012 10:32:34
%S A215136 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,
%T A215136 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,
%U A215136 4891,2,1,46,1,2,3,2,3,4,3,2,9,6,1,4,1,4,1,4,27
%N 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.
%C A215136 At least one iteration must be made.
%C A215136 Corresponding primes: 2, 5, 23, 11, 41, 17, 59, 23, 6197, 29, 68891, 311, 113, 41, 131, 47, 149, 53, 167, 59, ...
%e A215136 n=3: 3 => 8 => 23, so a(3)=2.
%e A215136 n=9: 9 => 26 => 77 => 230 => 689 => 2066 => 6197, so a(9)=6.
%o A215136 (Java)
%o A215136 import java.math.BigInteger;
%o A215136 public class A215136 {
%o A215136   public static void main (String[] args) {
%o A215136     long n, t, step;
%o A215136     BigInteger BI1 = BigInteger.valueOf(1);
%o A215136     BigInteger BI3 = BigInteger.valueOf(3);
%o A215136     for (n=1; n<3333; ++n) {
%o A215136       BigInteger bn = BigInteger.valueOf(n);
%o A215136       t = n;
%o A215136       for (step=1; step<9999; ++step) {
%o A215136         bn = bn.multiply(BI3).subtract(BI1);
%o A215136         t = (t*3+614889782588491409L) % 614889782588491410L;   // A002110(15)
%o A215136         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) ) {
%o A215136           if (bn.isProbablePrime(2)) {
%o A215136             if (bn.isProbablePrime(80)) break;
%o A215136           }
%o A215136         }
%o A215136       }
%o A215136       if (step==9999) System.out.printf("---(%d), ", n);
%o A215136       else            System.out.printf("%d, ", step);
%o A215136     }
%o A215136   }
%o A215136 }
%Y A215136 Cf. A000040, A078681.
%K A215136 nonn
%O A215136 1,3
%A A215136 _Alex Ratushnyak_, Aug 04 2012

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