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Numbers k such that 3^k - 34 is prime.
16

%I #21 Nov 11 2023 10:39:54

%S 4,7,11,13,29,32,36,44,79,157,197,341,467,996,1421,2479,3269,5203,

%T 7987,9341,14836,26047,47816,64304,100693,127597,167167,174697,182089,

%U 198791

%N Numbers k such that 3^k - 34 is prime.

%C a(31) > 2*10^5. - _Robert Price_, Nov 23 2013

%e For k = 4, 3^4 - 34 = 47 and 47 is prime. Hence k = 4 is included in the sequence.

%t Do[If[PrimeQ[3^n - 34], Print[n]], {n, 1, 10000}]

%t Select[Range[10000], PrimeQ[3^# - 34] &] (* _Alonso del Arte_, Nov 10 2012 *)

%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 1,1

%A _Nicolas M. Perrault_, Nov 10 2012

%E a(21)-a(30) from _Robert Price_, Nov 23 2013