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A241484 Primes p such that p+2 and p+4 are semiprime.

%I A241484 #9 Sep 08 2022 08:46:07
%S A241484 2,31,47,53,83,89,139,157,181,199,211,233,263,317,337,389,409,443,449,
%T A241484 467,541,577,587,631,677,683,719,751,787,811,839,919,947,991,1039,
%U A241484 1097,1117,1163,1187,1201,1259,1367,1381,1399,1559,1637,1669,1709,1759,1777,1847
%N A241484 Primes p such that p+2 and p+4 are semiprime.
%H A241484 K. D. Bajpai, <a href="/A241484/b241484.txt">Table of n, a(n) for n = 1..10000</a>
%e A241484 31 is prime and appears in the sequence because 31+2 = 33 = 3*11 and 31+4 = 35 = 5*7, which are semiprime.
%e A241484 53 is prime and appears in the sequence because 53+2 = 55 = 5*11 and 53+4 = 57 = 3*19, which are semiprime.
%p A241484 with(numtheory): KD:= proc() local a,b,d,k; k:=ithprime(n); a:=bigomega(k+2);b:=bigomega(k+4); if a=2 and  b=2 then RETURN (k); fi; end: seq(KD(), n=1..1000);
%t A241484 KD = {}; Do[t = Prime[n];If[PrimeOmega[t + 2] == 2 && PrimeOmega[t + 4] == 2,AppendTo[KD, t]], {n, 1000}]; KD
%o A241484 (Magma) IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(2000)| IsSemiprime(p+2) and IsSemiprime(p+4)]; // _Vincenzo Librandi_, Apr 24 2014
%Y A241484 Cf. A072381, A082919.
%K A241484 nonn
%O A241484 1,1
%A A241484 _K. D. Bajpai_, Apr 23 2014