|
%I #30 Jan 03 2016 04:38:54
%S 1,1,1,2,1,6,5,2,7,10,8
%N Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists.
%C The next terms after the missing a(11) are 31, 58, 4, 596, 3.
%e 3^3 * 1 + 1 = 28 is not a prime, 3^3 * 2^2 + 1 = 109 is a prime, so a(3) = 2.
%o (Java)
%o import java.math.BigInteger;
%o public class A228175 {
%o public static void main (String[] args) {
%o for (int n = 0; n < 333; n++) {
%o BigInteger nn = BigInteger.valueOf(n).pow(n);
%o int k = 1;
%o for (; k<10000; k++) {
%o BigInteger kk = BigInteger.valueOf(k).pow(k).multiply(nn).add(BigInteger.ONE);
%o if (kk.isProbablePrime(80)) {
%o System.out.printf("%d, ", k);
%o break;
%o }
%o }
%o if (k==10000) System.out.printf("- ");
%o }
%o }
%o }
%o (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 Cf. A000040, A000312, A156223.
%K nonn,hard,more
%O 0,4
%A _Alex Ratushnyak_, Nov 02 2013
| 