A219049 - OEIS

%I #19 Nov 12 2023 14:28:08

%S 5,8,18,21,69,84,181,216,461,642,672,2413,3681,5666,12281,14949,19508,

%T 27817,34061,43236,43733,81828

%N Numbers k such that 3^k - 32 is prime.

%C a(23) > 2*10^5. - _Robert Price_, Dec 22 2013

%e 3^5 - 32 = 211 (prime), so 5 is in the sequence.

%t Do[If[PrimeQ[3^n - 32], Print[n]], {n, 10000}]

%o (PARI) is(n)=isprime(3^n-32) \\ _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(15)-a(22) from _Robert Price_, Dec 22 2013