A219045 - OEIS

%I #20 Nov 12 2023 11:34:59

%S 7,10,13,22,27,30,57,62,117,255,535,651,873,998,1502,18145,22766,

%T 25770,43558,45663,48058,62887,87477,103585,115802

%N Numbers k such that 3^k - 26 is prime.

%C a(26) > 2*10^5. - _Robert Price_, Nov 20 2013

%e 3^7 - 26 = 2161 (prime), so 7 is in the sequence.

%t Do[If[PrimeQ[3^n - 26], Print[n]], {n, 3, 10000}]

%o (PARI) is(n)=isprime(3^n-26) \\ _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(25) from _Robert Price_, Nov 20 2013