A123924 - OEIS

%I #21 Aug 05 2021 12:26:55

%S 0,1,2,3,4,5,6,9,11,12,15,17,22,32,33,35,36,46,47,59,63,80,101,154,

%T 159,173,221,225,236,250,281,347,789,992,1607,1631,1983,2072,3616,

%U 3702,5076,5957,6335,8771,10203,10984,12203,12350,13660,14891

%N Numbers k such that 2^(k+1) + 3^k is prime.

%C Also numbers k such that A123601(k) = A085279(k+1) = 2^(k+1) + 3^k. There are only 4 known primes of form the 2^k + 3^k, {2, 5, 13, 97} = A082101, corresponding to k = {0, 1, 2, 4}.

%t Do[f=2^(n+1)+3^n;If[PrimeQ[f],Print[{n,f}]],{n,0,347}]

%t Select[Range[0,6400],PrimeQ[2^(#+1)+3^#]&] (* _Harvey P. Dale_, Mar 04 2019 *)

%o (PARI) is(n)=ispseudoprime(2^(n+1)+3^n) \\ _Charles R Greathouse IV_, Jun 13 2017

%Y Cf. A082101 (primes of form 2^k + 3^k), A085279, A123601 (smallest prime of the form p^n + q^n + r^n, where p,q,r are primes).

%K nonn

%O 1,3

%A _Alexander Adamchuk_, Nov 20 2006

%E More terms from _Stefan Steinerberger_, May 12 2007

%E a(44) from _Jinyuan Wang_, Aug 02 2021

%E a(45)-a(50) from _Michael S. Branicky_, Aug 05 2021