A166852 Numbers k such that k^k + 3 is prime.

2, 1036, 2770

Offset: 1

Author

Farideh Firoozbakht, Nov 20 2009

Keywords

• hard
• more
• nonn
• bref

Comments

Numbers corresponding to a(2) and a(3) are probable primes. 2770 is in the sequence so 2770^2770 + 3 is a probable prime; it is interesting that 277027703 is also prime. For the first term we have the same property: both 2^2 + 3 and 223 are prime.

For k = -1, k^k + 3 = 2 is prime but sequence focuses on the positive values of k. - Altug Alkan, Nov 28 2015

a(4) > 25000. - Michael S. Branicky, Oct 15 2024

Crossrefs

Cf. A087037, A100407, A100408, A166853.

Programs

Mathematica

Do[If[GCD[n,3]==1&&PrimeQ[n^n+3],Print[n]],{n,2,5362,2}]

PARI

is(n)=ispseudoprime(n^n+3) \\ Charles R Greathouse IV, Jun 13 2017