A172995 - OEIS

%I #30 Sep 07 2024 08:00:05

%S 1,3,7,75,191,395,891,2935,3855,59887,125447

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

%C The primes are in A172996.

%C Naturally these numbers are odd since 3^(2*k) + 7 = (8+1)^k + 7 == 0 (mod 8). - _Bruno Berselli_, Oct 08 2012

%C For n <= 9, (3^a(n) + 7)/2 has been proved prime using PARI's ECPP; a(10) corresponds to a BPSW PRP. a(11) > 10^5. - _Lucas A. Brown_, Feb 10 2021

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A172995.py">A172995.py</a>

%t Select[Range[5000], PrimeQ[(3^# + 7) / 2 ]&] (* _Vincenzo Librandi_, Oct 05 2012 *)

%o (PARI) is(n)=ispseudoprime((3^n+7)/2) \\ _Charles R Greathouse IV_, Jun 13 2017

%K nonn,hard,more

%O 1,2

%A _Vincenzo Librandi_, Feb 07 2010

%E a(7)-(9) from _Vincenzo Librandi_, Oct 05 2012

%E a(10) from _Lucas A. Brown_, Feb 10 2021

%E a(11) from _Michael S. Branicky_, Sep 07 2024