%I #11 Nov 01 2018 21:24:11

%S 3,19,31,101,139,167,1097,43151,60703,90499

%N Numbers k such that (3^k + 10^k)/13 is prime.

%C All terms are primes.

%C Next term is greater than 6700. - _Stefan Steinerberger_, May 11 2007

%C a(11) > 10^5. - _Robert Price_, Jan 15 2013

%t k=10; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

%o (PARI) is(n)=isprime((3^n+10^n)/13) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128070, A128071, A128072, A128073, A128074, A128075. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Feb 14 2007

%E a(7) from _Alexander Adamchuk_, Feb 14 2007

%E a(8)-a(10) from _Robert Price_, Jan 15 2013