A057900 Numbers k such that 3^k + k is prime.

2, 8, 34, 1532, 18248

Offset: 1

Author

Robert G. Wilson v, Nov 16 2000

Keywords

• nonn
• hard
• more

Comments

Note that if n > 2 and n+1 is prime then (by Fermat's theorem) n+1 divides 3^n+n.

If it exists, a(6) > 100000. - Hugo Pfoertner, Mar 01 2024

Crossrefs

Cf. A104743, A052007, A057909.

Programs

Mathematica

Do[ If[ PrimeQ[ 3^n + n ], Print[ n ] ], {n, 0, 3000} ]
v={2}; Do[If[EvenQ[n]&&Mod[n, 3]!=0&&!PrimeQ[n+1]&&PrimeQ[3^n+n], v=Append[v, n]; Print[v]], {n, 3, 19000}]
Select[Range[18500],PrimeQ[3^#+#]&] (* Harvey P. Dale, Jul 23 2013 *)

PARI

is(n)=ispseudoprime(3^n+n) \\ Charles R Greathouse IV, May 22 2017

Extensions

18248 from Farideh Firoozbakht, Aug 21 2003