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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.
0
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
Factorization in S_3 is not unique; for example, 220 = 4 * 55 = 10 * 22.
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
KEYWORD
nonn
AUTHOR
Gleb Ivanov, Oct 03 2021
STATUS
approved

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Last modified September 20 10:25 EDT 2024. Contains 376068 sequences. (Running on oeis4.)