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

2, 1036, 2770

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.

The prime corresponding to the next term, if it exists, has more than 20000 digits.

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) >= 14000. - Michael S. Branicky, Mar 21 2023

Links

Table of n, a(n) for n=1..3.

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

Cf. A087037, A100407, A100408, A166853.

Sequence in context: A196292 A182447 A218437 * A236951 A111203 A159858

Adjacent sequences: A166849 A166850 A166851 * A166853 A166854 A166855

Keyword

hard,more,nonn,bref

Author

Farideh Firoozbakht, Nov 20 2009

Status

approved