A373468 Primes such that x^16 = 2 has a solution in Z/pZ, but x^32 = 2 does not.

257, 2113, 2657, 7489, 10177, 15073, 18593, 23041, 25121, 25409, 25537, 25793, 27809, 30881, 30977, 32321, 37409, 38273, 41729, 43649, 51137, 51361, 54721, 59809, 63841, 67073, 67489, 75553, 77569, 83009, 86561, 92641, 94049, 94433, 95713, 101281, 102241

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Example

For p = 257, the equation x^16 = 2 has solutions 27, 41, 54, ... in Z/pZ, but x^32 can only be 0, +-1, +-4, +-16, +-64 (mod p).

Prog

(PARI) select( {is_A373468(p)=Mod(2, p)^(p\gcd(16, p-1))==1&&Mod(2, p)^(p\gcd(32, p-1))!=1}, primes(19999))
(Python)
from itertools import islice
from sympy import nextprime, is_nthpow_residue
def A373468_gen(startvalue=2): # generator of terms >= startvalue
    p = max(1, startvalue-1)
    while (p:=nextprime(p)):
        if is_nthpow_residue(2, 16, p) and not is_nthpow_residue(2, 32, p):
            yield p
A373468_list = list(islice(A373468_gen(), 10)) # Chai Wah Wu, Jun 23 2024

Crossrefs

Cf. A059287 (similar for x^8 vs x^16).

Subsequence of A070184 which is a subsequence of A252279.

Sequence in context: A070184 A054801 A173892 * A209533 A125648 A353941

Adjacent sequences: A373465 A373466 A373467 * A373469 A373470 A373471

Keyword

nonn

Author

M. F. Hasler, Jun 22 2024

Status

approved