A328660 Numbers k such that (10^k + 7^k)/17 is prime.

3, 5, 11, 19, 1259, 1399, 2539, 2843, 5857, 10589

Offset: 1

Author

Tim Johannes Ohrtmann, Oct 24 2019

Keywords

• nonn
• more
• hard

Comments

All terms are odd primes. Proof: a(n) cannot be even, because (10^(2*k) + 7^(2*k))/17 is not an integer. If odd number k = x*y, then (10^x + 7^x) and (10^y + 7^y) are nontrivial factors of (10^(x*y) + 7^(x*y)). In conclusion, a(n) must be odd and prime. - Daniel Suteu, Jan 22 2020

The corresponding primes are 79, 6871, 5998666279, 588905817363845479, ...

a(11) > 60000. - Michael S. Branicky, Jul 11 2024

Crossrefs

Cf. A001562, A128069, A217095.

Programs

Magma

[p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by Jinyuan Wang, Jan 22 2020

Mathematica

Select[Table[Prime[n], {n, 500}], PrimeQ[(10^#+7^#)/17] &] (* Modified by Jinyuan Wang, Jan 22 2020 *)

PARI

forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))