%I #10 Dec 09 2018 13:34:46

%S 2,3,5,7,11,13,17,41,43,47,61,79,89,101,107,139,157,181,199,239,271,

%T 307,311,331,337,347,349,379,397,409,421,431,479,487,499,521,523,541,

%U 571,607,613,641,643,661,673,701,719,761,769,811,823,829,839,877,881,883

%N Primes p such that p^3 - 2 is semiprime.

%H K. D. Bajpai, <a href="/A241716/b241716.txt">Table of n, a(n) for n = 1..9380</a>

%e 11 is prime and appears in the sequence because 11^3 - 2 = 1329 = 3 * 443, which is a semiprime.

%e 17 is prime and appears in the sequence because 17^3 - 2 = 4911 = 3 * 1637, which is a semiprime.

%e 23 is prime but does not appear in the sequence because 23^3 - 2 = 12165 = 3 * 5 * 811, which is not a semiprime.

%p with(numtheory):A241716:= proc() local k; k:=ithprime(x); if bigomega(k^3-2)=2 then RETURN (k); fi; end: seq(A241716(), x=1..500);

%t A241716 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 - 2] == 2, AppendTo[A241716, t]], {n, 500}]; A241716

%t Select[Prime[Range[200]],PrimeOmega[#^3-2]==2&] (* _Harvey P. Dale_, Dec 09 2018 *)

%Y Cf. A001358, A063637, A063638, A072381, A082919, A145292, A228183, A237627, A241483, A241493, A241659.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Apr 27 2014