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%I #22 Nov 09 2023 20:03:20
%S 3,4,5,8,17,19,29,124,304,640,1205,1549,1805,2492,2945,13075,20237,
%T 102763,173755,173828,174040
%N Numbers k such that 3^k - 14 is prime.
%C a(22) > 2*10^5. - _Robert Price_, Aug 31 2013
%t Do[If[PrimeQ[3^n - 14], Print[n]], {n, 3, 3000}]
%t Select[Range[1000], PrimeQ[3^# - 14] &] (* _Alonso del Arte_, Nov 10 2012 *)
%o (PARI) is(n)=isprime(3^n-14) \\ _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 1,1
%A _Nicolas M. Perrault_, Nov 10 2012
%E a(16)-a(21) from _Robert Price_, Aug 31 2013
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