A082387 Numbers k such that (5^k + 2^k)/7 is prime.

3, 17, 19, 47, 101, 1709, 2539, 5591, 6037, 8011, 19373, 26489, 27427

Offset: 1

Author

Hugo Pfoertner, May 22 2003

Keywords

• more
• nonn

Comments

Next term > 35000. - Giovanni Resta, Apr 06 2006

For (2^k + 5^k)/7 to be a prime, k must be a prime too. - Alexander Adamchuk, Feb 06 2007

No other terms less than 100000. - Robert Price, Apr 17 2012

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Examples

			a(1)=3 because (5^3 + 2^3)/7 = (125 + 8)/7 = 19 is prime.
		

Crossrefs

Cf. A057469 ((2^k + 3^k)/5 is prime).

Programs

Magma

[n : n in [1..10000] | IsPrime((5^n+2^n) div 7)]; // G. C. Greubel, Nov 02 2018

Mathematica

Do[f=(2^n+5^n)/7; If[PrimeQ[f], Print[{n, f}]], {n, 1, 35000}] (* Alexander Adamchuk, Feb 06 2007 *)
Select[Range[0, 10000], PrimeQ[(5^# + 2^#)/7] &] (* G. C. Greubel, Nov 02 2018 *)

PARI

is(n)=ispseudoprime((5^n + 2^n)/7) \\ Charles R Greathouse IV, Apr 28 2015

Extensions

More terms from Hugo Pfoertner, Jun 23 2003

More terms from Giovanni Resta, Apr 06 2006