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

1,1

Links

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

Example

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).

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 *)

Prog

(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

Crossrefs

Cf. A001358, A014612, A109611, A175634.

Sequence in context: A358574 A084488 A337877 * A001749 A175786 A258848

Adjacent sequences: A211407 A211408 A211409 * A211411 A211412 A211413

Keyword

nonn,easy

Author

Jonathan Vos Post, Feb 09 2013

Status

approved