A221865 The nonprimes k such that k + 2 is either a prime or a semiprime.

0, 1, 4, 8, 9, 12, 15, 20, 21, 24, 27, 32, 33, 35, 36, 39, 44, 45, 49, 51, 55, 56, 57, 60, 63, 65, 69, 72, 75, 77, 80, 81, 84, 85, 87, 91, 92, 93, 95, 99, 104, 105, 111, 116, 117, 119, 120, 121, 125, 129, 132, 135, 140, 141, 143, 144, 147, 153, 155, 156, 159, 161, 164, 165, 171, 175, 176, 177, 183

Offset: 1

Author

Gerasimov Sergey, Apr 18 2013

Keywords

• nonn

Comments

Chen primes A109611(n) such that A109611(n)-/+ a(n) are both prime: 2, 29, 53, 113, 139,...

Unrelated: Numbers n such that n + 2^bigomega(n) is either a prime or a semiprime: 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 22, 23, 25, 27,...

A179384 is a subsequence. - R. J. Mathar, Apr 26 2013

Crossrefs

Cf. A001358, A109611, A175634.

Programs

Maple

A221865 := proc(n)
    option remember;
    if n =1 then
        0;
    else
        for a from procname(n-1)+1 do
            if not isprime(a) then
            if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
                return a;
            end if;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Apr 26 2013

Mathematica

Select[Range[0,200],!PrimeQ[#]&&PrimeOmega[#+2]<3&] (* Harvey P. Dale, May 05 2013 *)

Extensions

Corrected by R. J. Mathar, Apr 26 2013