A228175 Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists.
1, 1, 1, 2, 1, 6, 5, 2, 7, 10, 8
Offset: 0
Examples
3^3 * 1 + 1 = 28 is not a prime, 3^3 * 2^2 + 1 = 109 is a prime, so a(3) = 2.
Programs
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Java
import java.math.BigInteger; public class A228175 { public static void main (String[] args) { for (int n = 0; n < 333; n++) { BigInteger nn = BigInteger.valueOf(n).pow(n); int k = 1; for (; k<10000; k++) { BigInteger kk = BigInteger.valueOf(k).pow(k).multiply(nn).add(BigInteger.ONE); if (kk.isProbablePrime(80)) { System.out.printf("%d, ", k); break; } } if (k==10000) System.out.printf("- "); } } }
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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
Formula
a(n) = A231119(n^n). - Jason Yuen, Nov 15 2024
Comments