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A211410 Chen triprimes, triprimes (A014612) m such that m+2 is either prime or semiprime.

%I A211410 #18 Jul 15 2019 15:34:14
%S A211410 8,12,20,27,44,45,63,75,92,99,105,116,117,125,147,153,164,165,171,175,
%T A211410 195,207,212,231,245,255,261,275,279,285,325,332,333,345,356,357,363,
%U A211410 369,387,399,425,429,435,452,455,465,477,483,507,524
%N A211410 Chen triprimes, triprimes (A014612) m such that m+2 is either prime or semiprime.
%H A211410 Charles R Greathouse IV, <a href="/A211410/b211410.txt">Table of n, a(n) for n = 1..10000</a>
%e A211410 27=3^3 and 45=3^2*9 are in the sequence because 27+2 = 29 and 45+2 = 47 are primes.
%e A211410 8=2^3, 12=2^2*3, and 20=2^2*5 are in the sequence because 8+2=10=2*5, 12+2=14=2*7, and 20+2=22=2*11 are semiprimes (A001358).
%p A211410 A211410 := proc(n)
%p A211410     option remember;
%p A211410     local a;
%p A211410     if n = 1 then
%p A211410         8;
%p A211410     else
%p A211410         for a from procname(n-1)+1 do
%p A211410             if numtheory[bigomega](a) = 3 then
%p A211410                 if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
%p A211410                     return a;
%p A211410                 end if;
%p A211410             end if;
%p A211410         end do:
%p A211410     end if;
%p A211410 end proc:
%p A211410 seq(A211410(n),n=1..80) ; # _R. J. Mathar_, Feb 10 2013
%t A211410 Select[Range[600],PrimeOmega[#]==3&&PrimeOmega[#+2]<3&] (* _Harvey P. Dale_, Jul 15 2019 *)
%o A211410 (PARI) issemi(n)=bigomega(n)==2
%o A211410 list(lim)=my(v=List(),pq); forprime(p=2,lim\4, forprime(q=2,min(lim\2\p,p), pq=p*q; forprime(r=2,min(lim\pq,q), if(isprime(pq*r+2) || issemi(pq*r+2), listput(v,pq*r))))); Set(v) \\ _Charles R Greathouse IV_, Aug 23 2017
%Y A211410 Cf. A001358, A014612, A109611, A175634.
%K A211410 nonn,easy
%O A211410 1,1
%A A211410 _Jonathan Vos Post_, Feb 09 2013