A348156 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.

4, 7, 10, 13, 19, 22, 25, 31, 34, 37, 43, 46, 55, 58, 61, 67, 73, 79, 82, 85, 94, 97, 103, 106, 109, 115, 118, 121, 127, 139, 142, 145, 151, 157, 163, 166, 178, 181, 187, 193, 199, 202, 205, 211, 214, 223, 226, 229, 235, 241, 253, 262, 265, 271, 274, 277, 283, 289, 295, 298

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..60.

Mathematica

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}]]]]

Prog

(PARI) isok(m) = ((m % 3)==1) && (#select(x->((x%3)==1), divisors(m)) == 2); \\ Michel Marcus, Oct 06 2021
(Python)
nn = 300
s = [True]*((nn)//3 + 1)
for i in range(4, nn, 3):
    if s[(i-1)//3]:
        for t in range(4, (nn)//i, 3):
            s[(i*t-1)//3] = False
print([3*i + 1 for i in range(1, (nn + 3)//3) if s[i]])

Crossrefs

Cf. A016777, A057948, A054520.

Sequence in context: A310686 A339637 A173178 * A287555 A008470 A002640

Adjacent sequences: A348153 A348154 A348155 * A348157 A348158 A348159

Keyword

nonn

Author

Gleb Ivanov, Oct 03 2021

Status

approved