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

8, 12, 20, 27, 44, 45, 63, 75, 92, 99, 105, 116, 117, 125, 147, 153, 164, 165, 171, 175, 195, 207, 212, 231, 245, 255, 261, 275, 279, 285, 325, 332, 333, 345, 356, 357, 363, 369, 387, 399, 425, 429, 435, 452, 455, 465, 477, 483, 507, 524

Offset: 1

Author

Jonathan Vos Post, Feb 09 2013

Keywords

• nonn
• easy

Examples

			27=3^3 and 45=3^2*9 are in the sequence because 27+2 = 29 and 45+2 = 47 are primes.
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).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A014612, A109611, A175634.

Programs

Maple

A211410 := proc(n)
    option remember;
    local a;
    if n = 1 then
        8;
    else
        for a from procname(n-1)+1 do
            if numtheory[bigomega](a) = 3 then
                if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
                    return a;
                end if;
            end if;
        end do:
    end if;
end proc:
seq(A211410(n),n=1..80) ; # R. J. Mathar, Feb 10 2013

Mathematica

Select[Range[600],PrimeOmega[#]==3&&PrimeOmega[#+2]<3&] (* Harvey P. Dale, Jul 15 2019 *)

PARI

issemi(n)=bigomega(n)==2
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