login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 16:18 EDT 2022. Contains 356215 sequences. (Running on oeis4.)