login
Numbers k such that 3^k - 22 is prime.
16

%I #27 Nov 12 2023 11:35:06

%S 3,4,9,13,28,45,46,184,285,688,697,1257,1785,2368,3721,7444,51613

%N Numbers k such that 3^k - 22 is prime.

%C a(18) > 2*10^5. - _Robert Price_, Oct 18 2013

%e 3^3 - 22 = 5 (prime), so 3 is in the sequence.

%t Do[If[PrimeQ[3^n - 22], Print[n]], {n, 10000}]

%o (PARI) is(n)=isprime(3^n-22) \\ _Charles R Greathouse IV_, Feb 17 2017

%o (Python)

%o from sympy import isprime

%o def ok(n): return isprime(3**n - 22)

%o print([m for m in range(700) if ok(m)]) # _Michael S. Branicky_, Mar 04 2021

%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(17) from _Robert Price_, Oct 18 2013