A058911 Numbers k such that k^k + k + 1 is prime.

0, 1, 2, 3, 6, 9, 462

Offset: 1

Author

Felice Russo, Jan 10 2001

Keywords

• nonn
• hard
• more

Comments

There is no further term up to 10000. - Farideh Firoozbakht, Nov 11 2006

If it exists, a(8) > 32100. - Dmitry Petukhov, Sep 14 2021

Examples

			a(2) = 2 because 2^2 + 2 + 1 = 7.
		

Crossrefs

Cf. A058912 (k^k + k - 1 is prime), A161471 (corresponding primes).

Programs

Mathematica

Do[ If[ PrimeQ[ n^n + n + 1], Print[n]], {n, 1, 700} ]
Join[{0},Select[Range[470],PrimeQ[#^#+#+1]&]] (* Harvey P. Dale, Dec 11 2022 *)

PARI

f2(n,k) = for(x=1,n,y=x^x+x+k;if(ispseudoprime(y),print1(x","))) \\ Cino Hilliard, Jan 07 2005

PFGW

ABC2 $a^$a + $a + 1
a: from 0 to 1000 // Jinyuan Wang, Mar 01 2020