A109387 Numbers k such that 3^k - k^3 is prime.

1, 4, 10, 52, 112, 212, 346, 406, 512, 13904, 76610, 89746, 114892

Offset: 1

Author

Ryan Propper, Jun 26 2005

Keywords

• hard
• more
• nonn

Comments

Terms <= 512 correspond to certified primes. Next term after 13904 is greater than 20000.

Examples

			4 is a term because 3^4 - 4^3 = 17 is prime.
3^10 - 10^3 = 58049 is prime, hence 10 is a term.
		

Programs

Mathematica

Do[If[PrimeQ[3^n - n^3], Print[n]], {n, 1, 20000}]

PARI

is(n)=isprime(3^n-n^3) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

Two more terms from Donovan Johnson, Feb 26 2008

a(13) from Norbert Schneider submitted by Robert Price, Mar 16 2019