login
Semiprimes of the form 3^n - 2^n.
1

%I #14 Jul 09 2023 09:40:08

%S 65,2059,19171,1586131,1161737179,94134790219,450283768452043891,

%T 7509466514977363620705281135650699,

%U 2909321189362570189660446183802104997118371,19088056323407826916968161259086927505582748291

%N Semiprimes of the form 3^n - 2^n.

%H Dario Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%e a(1)=65 because 3^4-2^4=65=5*13 is a semiprime; a(3)=19171: 3^9-2^9=19171=19*1009.

%t Select[Table[3^n - 2^n, {n, 100}], PrimeOmega[#] == 2&] (* _Vincenzo Librandi_, Sep 21 2012 *)

%o (Magma) IsSemiprime:=func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [2..100] | IsSemiprime(s) where s is 3^n - 2^n]; // _Vincenzo Librandi_, Sep 21 2012

%Y Cf. A082869 = n such that 3^n-2^n is a semiprime, A058765 primes of the form 3^n-2^n.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jun 03 2004

%E a(10) from _Vincenzo Librandi_, Sep 21 2012