cp's OEIS Frontend

A228175 Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists.

%I A228175 #43 Feb 28 2025 05:53:33
%S A228175 1,1,1,2,1,6,5,2,7,10,8
%N A228175 Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists.
%C A228175 The next terms after the missing a(11) are 31, 58, 4, 596, 3.
%C A228175 a(11) > 20000 or a(11) = 0, a(17) = 4308, a(18) = 1073, a(19) > 20000 or a(19) = 0. - _Jason Yuen_, May 21 2024
%C A228175 a(11) > 10^5 or a(11) = 0. a(19) > 10^5 or a(19) = 0. - _Jason Yuen_, Feb 27 2025
%F A228175 a(n) = A231119(n^n). - _Jason Yuen_, Nov 15 2024
%e A228175 3^3 * 1 + 1 = 28 is not a prime, 3^3 * 2^2 + 1 = 109 is a prime, so a(3) = 2.
%o A228175 (Java)
%o A228175 import java.math.BigInteger;
%o A228175 public class A228175 {
%o A228175   public static void main (String[] args) {
%o A228175     for (int n = 0; n < 333; n++) {
%o A228175       BigInteger nn = BigInteger.valueOf(n).pow(n);
%o A228175       int k = 1;
%o A228175       for (; k<10000; k++) {
%o A228175         BigInteger kk = BigInteger.valueOf(k).pow(k).multiply(nn).add(BigInteger.ONE);
%o A228175         if (kk.isProbablePrime(80)) {
%o A228175           System.out.printf("%d, ", k);
%o A228175           break;
%o A228175         }
%o A228175       }
%o A228175       if (k==10000) System.out.printf("- ");
%o A228175     }
%o A228175   }
%o A228175 }
%o A228175 (PARI) A228175(n,L=9e9,s=1)={forstep(k=s+(bittest(n,0)&&n>1&&bittest(s,0)), L, 1+bittest(n,0), ispseudoprime(n^n*k^k+1)&&return(k))} \\ Optional args allow specification of start and limit for search; for odd n > 1, only check even k. - _M. F. Hasler_, Nov 03 2013
%Y A228175 Cf. A000040, A000312, A156223, A231119, A380903.
%K A228175 nonn,hard,more
%O A228175 0,4
%A A228175 _Alex Ratushnyak_, Nov 02 2013