A241732 - OEIS

%I #13 Jun 20 2019 13:36:18

%S 2,11,13,17,41,89,101,239,271,331,571,641,719,1051,1231,1321,1549,

%T 1559,1721,1741,1831,1993,1999,2029,2311,2459,2749,2837,2861,2939,

%U 3389,3467,3671,4049,4111,4273,4787,4919,4969,5657,5689,5861,6221,6679,6691,6829,7109

%N Primes p such that p^3 + 2 and p^3 - 2 are semiprime.

%H K. D. Bajpai, <a href="/A241732/b241732.txt">Table of n, a(n) for n = 1..2310</a>

%e 11 is prime and appears in the sequence because 11^3 + 2 = 1333 = 31 * 43 and 11^3 - 2 = 1329 = 3 * 443, both are semiprime.

%e 41 is prime and appears in the sequence because 41^3 + 2 = 68923 = 157 * 439 and 41^3 - 2 = 68919 = 3 * 22973, both are semiprime.

%p with(numtheory): KD:= proc() local k; k:=ithprime(n); if bigomega(k^3+2)=2 and bigomega(k^3-2)=2 then k; fi; end: seq(KD(), n=1..2000);

%t A241732 = {}; Do[t = Prime[n]; If[PrimeOmega[t^3 + 2] == 2 && PrimeOmega[t^3 - 2] == 2, AppendTo[A241732, t]], {n, 500}]; A241732

%t Select[Prime[Range[1000]],PrimeOmega[#^3+2]==PrimeOmega[#^3-2]==2&] (* _Harvey P. Dale_, Jun 20 2019 *)

%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