%I #8 Apr 27 2014 12:24:25

%S 2,11,13,17,19,23,31,41,53,59,89,101,131,137,149,193,211,223,227,229,

%T 233,239,251,271,293,317,331,359,401,449,461,557,563,571,593,599,619,

%U 641,659,677,691,719,739,751,809,821,853,929,971,991,1009,1013,1039,1051

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

%H K. D. Bajpai, <a href="/A241659/b241659.txt">Table of n, a(n) for n = 1..10000</a>

%e 11 is prime and appears in the sequence because 11^3 + 2 = 1333 = 31 * 43, which is a semiprime.

%e 17 is prime and appears in the sequence because 17^3 + 2 = 4915 = 5 * 983, which is a semiprime.

%e 37 is prime but does not appear in the sequence because 37^3 + 2 = 50655 = 3 * 5 * 11 * 983, which is not a semiprime.

%p with(numtheory): KD:= proc() local a, b, k; k:=ithprime(n); a:=bigomega(k^3+2); if a=2 then RETURN (k); fi; end: seq(KD(), n=1..500);

%t A241659 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2, AppendTo[A241659, t]], {n, 500}]; A241659

%t (*For the b-file*) c = 0; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2, c++; Print[c, " ", t]], {n, 1,6*10^4}];

%o (PARI) s=[]; forprime(p=2, 1200, if(bigomega(p^3+2)==2, s=concat(s, p))); s \\ _Colin Barker_, Apr 27 2014

%Y Cf. A001358, A063637, A063638, A228183, A237627, A241483, A241493.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Apr 26 2014