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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..10.

Mathematica

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

Prog

(PARI) forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))
(Magma) [p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by Jinyuan Wang, Jan 22 2020

Crossrefs

Cf. A001562, A128069, A217095.

Sequence in context: A092672 A061068 A263925 * A058932 A118037 A377249

Adjacent sequences: A328657 A328658 A328659 * A328661 A328662 A328663

Keyword

nonn,more,hard

Author

Tim Johannes Ohrtmann, Oct 24 2019

Status

approved