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A228175 Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists. 2
1, 1, 1, 2, 1, 6, 5, 2, 7, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The next terms after the missing a(11) are 31, 58, 4, 596, 3.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

3^3 * 1 + 1 = 28 is not a prime, 3^3 * 2^2 + 1 = 109 is a prime, so a(3) = 2.

PROG

(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("- ");

    }

  }

}

(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

CROSSREFS

Cf. A000040, A000312, A156223.

Sequence in context: A295517 A070918 A113381 * A118980 A090665 A021826

Adjacent sequences:  A228172 A228173 A228174 * A228176 A228177 A228178

KEYWORD

nonn,hard,more

AUTHOR

Alex Ratushnyak, Nov 02 2013

STATUS

approved

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Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)