OFFSET
1,1
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
MATHEMATICA
Do[If[GCD[n, 3]==1&&PrimeQ[n^n+3], Print[n]], {n, 2, 5362, 2}]
PROG
(PARI) is(n)=ispseudoprime(n^n+3) \\ Charles R Greathouse IV, Jun 13 2017
CROSSREFS
KEYWORD
hard,more,nonn,bref
AUTHOR
Farideh Firoozbakht, Nov 20 2009
STATUS
approved