A348156 - OEIS

%I #25 Dec 04 2021 12:52:40

%S 4,7,10,13,19,22,25,31,34,37,43,46,55,58,61,67,73,79,82,85,94,97,103,

%T 106,109,115,118,121,127,139,142,145,151,157,163,166,178,181,187,193,

%U 199,202,205,211,214,223,226,229,235,241,253,262,265,271,274,277,283,289,295,298

%N S_3-primes: let S_3 = {1,4,7,...,3i+1,...}; then an S_3-prime is in S_3 but is not divisible by any elements of S_3 except for itself and 1.

%C Factorization in S_3 is not unique; for example, 220 = 4 * 55 = 10 * 22.

%t nn = 100; Complement[Table[3 k + 1, {k, 1, nn}], Union[Flatten[ Table[Table[(3 k + 1) (3 j + 1), {k, 1, j}], {j, 1, nn}]]]]

%o (PARI) isok(m) = ((m % 3)==1) && (#select(x->((x%3)==1), divisors(m)) == 2); \\ _Michel Marcus_, Oct 06 2021

%o (Python)

%o nn = 300

%o s = [True]*((nn)//3 + 1)

%o for i in range(4, nn, 3):

%o     if s[(i-1)//3]:

%o         for t in range(4, (nn)//i, 3):

%o             s[(i*t-1)//3] = False

%o print([3*i + 1 for i in range(1, (nn + 3)//3) if s[i]])

%Y Cf. A016777, A057948, A054520.

%K nonn

%O 1,1

%A _Gleb Ivanov_, Oct 03 2021