%I #18 Sep 19 2024 04:18:17
%S 3,7,127,283,883,1523,4001
%N Numbers k such that (2^k + 9^k)/11 is prime.
%C All terms are primes. Note that first 3 terms {3, 7, 127} are primes of the form 2^q - 1, where q = {2, 3, 7} is prime too. Corresponding primes of the form (2^k + 9^k)/11 are {67, 434827, ...}.
%C a(8) > 10^5. - _Robert Price_, Dec 23 2012
%t Do[p=Prime[n];f=(2^p+9^p)/11; If[PrimeQ[f], Print[{p, f}]], {n, 1, 100}]
%o (PARI) is(n)=ispseudoprime((2^n+9^n)/11) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y Cf. A000978 = numbers n such that (2^n + 1)/3 is prime.
%Y Cf. A057469 = numbers n such that (2^n + 3^n)/5 is prime.
%Y Cf. A082387 = numbers n such that (2^n + 5^n)/7 is prime.
%K hard,more,nonn,changed
%O 1,1
%A _Alexander Adamchuk_, Feb 06 2007
%E 2 more terms from _Rick L. Shepherd_, Feb 14 2007
%E a(7) from _Robert Price_, Dec 23 2012