A014755 3 and -3 are both 4th powers (one implies other) mod these primes p=1 mod 8.

193, 313, 433, 577, 601, 673, 769, 937, 1201, 1297, 1321, 1657, 1801, 1993, 2137, 2473, 2521, 2593, 2833, 2953, 3169, 3529, 3673, 3697, 3769, 3889, 4057, 4129, 4153, 4297, 4441, 4513, 4561, 4801, 4969, 5113, 5209, 5233, 5281, 5449, 5521

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(p) isprime(p) and [msolve(x^4=3, p)] <> [] end proc:
select(filter, [seq(i, i=1..10^4, 8)]); # Robert Israel, May 07 2019

Mathematica

okQ[p_] := PrimeQ[p] && Solve[x^4 == 3, x, Modulus -> p] != {};
Select[Range[1, 10000, 8], okQ] (* Jean-François Alcover, Feb 08 2023 *)

Prog

(PARI) forprime(p=1, 9999, p%8==1&&ispower(Mod(3, p), 4)&&print1(p", ")) \\ M. F. Hasler, Feb 18 2014
(PARI) is_A014755(p)={p%8==1&&ispower(Mod(3, p), 4)&&isprime(p)} \\ M. F. Hasler, Feb 18 2014
(Python)
from itertools import count, islice
from sympy import nextprime, is_nthpow_residue
def A014755_gen(startvalue=2): # generator of terms >= startvalue
    p = max(nextprime(startvalue-1), 2)
    while True:
        if p&7==1 and is_nthpow_residue(3, 4, p) and is_nthpow_residue(-3, 4, p):
            yield p
        p = nextprime(p)
A014755_list = list(islice(A014755_gen(), 20)) # Chai Wah Wu, May 02 2024

Crossrefs

Cf. A007519.

Sequence in context: A015988 A260539 A142743 * A238667 A216451 A139506

Adjacent sequences: A014752 A014753 A014754 * A014756 A014757 A014758

Keyword

nonn

Author

Warren D. Smith

Extensions

Offset changed from 0 to 1 by Bruno Berselli, Feb 20 2014

Status

approved