A182373 - OEIS

%I #40 Sep 23 2024 01:59:48

%S 3,5,7,37,45,53,179,277,721,2087,6197,6317,8775,12781,38943,47273,

%T 50507,66693

%N Positive integers k such that k*3^k - 2 is prime.

%C Similar to A060353, and to the Woodall primes, A050918. The next term in the sequence is unknown; if the sequence is infinite, the next term is greater than 5000.

%C a(15) > 30000. - _Tyler NeSmith_, Apr 22 2022

%C a(19) > 10^5. - _Michael S. Branicky_, Sep 22 2024

%e 79 = 3*3^3 - 2; 1213 = 5*3^5 - 2; 15307 = 7*3^7 - 2.

%p #choose N large, then S is the desired set

%p f:=n->n*3^n - 2:

%p S:={}:

%p for n from 0 to N do if(isprime(f(n))) then S:=S union {n}: fi: od

%t Select[Range[2100], PrimeQ[#*3^# - 2] &] (* _Jayanta Basu_, Jun 01 2013 *)

%o (PARI) for(n=1, 1e6, if(ispseudoprime(3^n*n - 2), print1(n, ", "))) \\ _Altug Alkan_, Dec 01 2015

%Y Cf. A050918, A060353.

%K nonn,more

%O 1,1

%A _Patrick Devlin_, Apr 26 2012

%E a(11)-a(14) from _Altug Alkan_, Dec 01 2015

%E a(15)-a(17) from _Michael S. Branicky_, Apr 23 2023

%E a(18) from _Michael S. Branicky_, Sep 22 2024