%I #34 Nov 29 2022 02:41:21

%S 4,12,18,26,106,164,246,956,2554,3350,6496,8706,9008,15398,15490,

%T 20408,39240,41060,41842,58358,60346,82214,134972,194014,344204,

%U 587712,778070

%N Numbers k such that (3^k - 7)/2 is prime.

%C x = 3^k is a solution to sigma(x - 7) = sigma(x) - 7 when (3^k - 7)/2 is prime.

%C a(28) > 10^6

%e (3^4 - 7)/2 = 37 is prime, so 4 is in the sequence.

%p with(numtheory):i := 0:x := 1:while i < 1000 do i := i+1:x := 3*x: if isprime((x-7)/2) then print(i):fi:od:

%t Do[ If[ PrimeQ[ (3^n - 7)/2 ], Print[n] ], {n, 2, 5500} ]

%t Select[Range[2, 10000], PrimeQ[((3^# - 7)/2)] &] (* _Vincenzo Librandi_, Sep 30 2012 *)

%o (PARI) is(n)=ispseudoprime((3^n-7)/2) \\ _Charles R Greathouse IV_, May 22 2017

%Y Cf. A000203, A063680, A015913-A015917, A054905, A116970.

%K nonn,more

%O 1,1

%A _Jud McCranie_, Jul 28 2001

%E More terms from _Robert G. Wilson v_, Aug 02 2001

%E 0, 1 removed and a(11)-a(13) added from _Vincenzo Librandi_, Sep 30 2012

%E a(14)-a(17) from _Seth A. Troisi_, Oct 17 2022

%E a(17) corrected, a(18)-a(25) from _Seth A. Troisi_, Oct 29 2022

%E a(26)-a(27) from _Seth A. Troisi_, Nov 28 2022