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%I #17 Sep 08 2022 08:46:24
%S 3,5,11,19,1259,1399,2539,2843,5857,10589
%N Numbers k such that (10^k + 7^k)/17 is prime.
%C 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
%C The corresponding primes are 79, 6871, 5998666279, 588905817363845479, ...
%t Select[Table[Prime[n], {n, 500}], PrimeQ[(10^#+7^#)/17] &] (* Modified by _Jinyuan Wang_, Jan 22 2020 *)
%o (PARI) forprime(k=3, 10000, if(isprime((10^k+7^k)/17), print1(k, ", ")))
%o (Magma) [p: p in PrimesUpTo(1000) | IsPrime((10^p+7^p) div 17)]; // Modified by _Jinyuan Wang_, Jan 22 2020
%Y Cf. A001562, A128069, A217095.
%K nonn,more,hard
%O 1,1
%A _Tim Johannes Ohrtmann_, Oct 24 2019
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