cp's OEIS Frontend

A231119 Least positive k such that n * k^k + 1 is a prime, or 0 if no such k exists.

%I A231119 #31 May 28 2025 19:23:28
%S A231119 1,1,2,1,102414,1,2,17,2,1,36,1,2,3,2,1,210,1,20,3,990,1,6,2,2,6,2,1
%N A231119 Least positive k such that n * k^k + 1 is a prime, or 0 if no such k exists.
%C A231119 The number a(5) is conjectured to be zero. Four days of computation have shown that all numbers 5*k^k+1 are composite for k = 1..22733. - _T. D. Noe_, Nov 11 2013
%C A231119 The sum of 1/log(n*k^k) diverges slowly for every n so normal heuristics predict infinitely many primes in each case, including n=5. - _Jens Kruse Andersen_, Jun 16 2014
%C A231119 a(5) > 100000 or a(5) = 0. a(29) > 100000 or a(29) = 0. - _Jason Yuen_, Jan 06 2025
%C A231119 a(5) = 102414 . - _Phillip Poplin_, May 27 2025
%C A231119 a(29) > 150000 or a(29) = 0. - _Phillip Poplin_, May 27 2025
%o A231119 (Java)
%o A231119 import java.math.BigInteger; public class A231119 { public static void main (String[] args) { for (int n = 1; n < 3333; n++) { BigInteger nn = BigInteger.valueOf(n); for (int k=1; k<10000; k++) { BigInteger p = nn.multiply(BigInteger.valueOf(k).pow(k)).add(BigInteger.ONE); if (p.isProbablePrime(80)) { System.out.printf("%d, ", k); break; } else System.out.printf("."); } } } }
%Y A231119 Cf. A035093, A057217, A175763, A228175.
%K A231119 nonn,hard,more
%O A231119 1,3
%A A231119 _Alex Ratushnyak_, Nov 04 2013
%E A231119 a(5) from _Phillip Poplin_, May 27 2025