A163184 Primes of the form 8k + 1 dividing 2^j + 1 for some odd j.

281, 617, 1033, 1049, 1097, 1193, 1481, 1553, 1753, 1777, 2281, 2393, 2473, 2657, 2833, 2857, 3049, 3529, 3673, 3833, 4049, 4153, 4217, 4273, 4457, 4937, 5113, 5297, 5881, 6121, 6449, 6481, 6521, 6529, 6569, 6761, 6793, 6841, 7121, 7129, 7481, 7577, 7817, 8081, 8233, 8537, 9001, 9137, 9209, 9241

Offset

1,1

Comments

Each term p has the form 2^r*j + 1, where r >= 3, j is odd, and ord_p(-2) divides j.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

281 is in the sequence as 281 = 2^3*35 + 1 and 281 | 2^35 + 1.

Maple

with(numtheory):A:=NULL:p:=2: for c to 500 do p:=nextprime(p); if order(-2, p) mod 2=1 and p mod 8 = 1 then A:=A, p;; fi; od:A;
# Alternative:
q:= n-> isprime(n) and irem(numtheory[order](-2, n), 2)=1:
select(q, [1+8*k$k=1..1155])[];  # Alois P. Heinz, Feb 05 2026

Prog

(Python)
from sympy import n_order, nextprime
from itertools import islice
def A163184_gen(): # generator of terms
    p = 3
    while True:
        if p&7==1 and n_order(-2, p)&1:
            yield p
        p = nextprime(p)
A163184_list = list(islice(A163184_gen(), 20)) # Chai Wah Wu, Feb 05 2026

Crossrefs

Set difference of A163183 and A007520.

Subsequence of A033203, A051071, A051073, A051077, A051085, A051101.

Sequence in context: A056215 A142397 A142546 * A122710 A161191 A108836

Adjacent sequences: A163181 A163182 A163183 * A163185 A163186 A163187

Keyword

easy,nonn

Author

Christopher J. Smyth, Jul 22 2009

Extensions

More terms from Max Alekseyev, Sep 29 2016

Status

approved