A199859 Numbers k such that 6k-5 is a composite number of the form (6x-5)*(6y-5) when x or y is not equal to 1 except for k=1.

1, 9, 16, 23, 29, 30, 37, 42, 44, 51, 55, 58, 61, 65, 68, 72, 79, 80, 81, 86, 93, 94, 99, 100, 105, 107, 114, 118, 120, 121, 128, 130, 133, 135, 137, 142, 146, 149, 155, 156, 159, 161, 163, 170, 172, 175, 177, 180, 184, 185, 191, 192, 194, 198, 205, 211, 212

Offset: 0

Author

Eleonora Echeverri-Toro, Nov 11 2011

Keywords

• nonn
• easy

Comments

Numbers whose associate in A091300 has at least one nontrivial factorization into two factors of A016921.

Crossrefs

Cf. A091300.

Programs

Maple

isA016921 := proc(n)
    (n mod 6)=1 ;
end proc:
isA091300 := proc(n)
    (not isprime(n)) and isA016921(n) ;
end proc:
isA199859 := proc(n)
    if n = 1 then
        return true;
    elif isA091300(6*n-5) then
        for d in numtheory[divisors](6*n-5) minus {1,6*n-5} do
            if isA016921(d) and isA016921((6*n-5)/d) then
                return true;
            end if;
        end do:
        return false;
    else
        return false;
    end if;
end proc:
for n from 1 to 210 do
    if isA199859(n) then
        printf("%d,",n) ;
    end if ;
end do; # R. J. Mathar, Nov 25 2011