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%I #21 Nov 12 2023 14:28:17
%S 1,2,3,5,7,9,10,17,27,34,51,57,61,89,98,171,547,569,769,874,1105,2198,
%T 2307,3937,4685,5105,5582,11131,11821,15902,24626,36401,46195,50974,
%U 65198,66685
%N Numbers k such that 3^k + 34 is prime.
%C a(37) > 2*10^5. - _Robert Price_, Nov 24 2013
%e For k = 2, 3^2 + 34 = 43 (prime), so 2 is in the sequence.
%t Do[If[PrimeQ[3^n + 34], Print[n]], {n, 10000}]
%o (PARI) is(n)=isprime(3^n+34) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. Sequences of numbers k such that 3^k + m is prime:
%Y (m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
%Y (m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
%Y (m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
%Y (m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
%Y (m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
%Y (m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.
%K nonn,more
%O 1,2
%A _Nicolas M. Perrault_, Nov 10 2012
%E a(28)-a(36) from _Robert Price_, Nov 24 2013