A057129 -4 is a square mod n.

1, 2, 4, 5, 8, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 50, 52, 53, 58, 61, 65, 68, 73, 74, 82, 85, 89, 97, 100, 101, 104, 106, 109, 113, 116, 122, 125, 130, 136, 137, 145, 146, 148, 149, 157, 164, 169, 170, 173, 178, 181, 185, 193, 194, 197, 200, 202, 205, 212

Offset: 1

Author

Henry Bottomley, Aug 10 2000

Keywords

• nonn

Comments

Numbers that are not multiples of 16 and for which all odd prime factors are congruent to 1 mod 4. - Eric M. Schmidt, Apr 21 2013

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Crossrefs

Includes the primes in A002313 and these (primes congruent to {1, 2} mod 4) are the prime factors of the terms in this sequence. Cf. A008784, A057125, A057126, A057127, A057128.

Programs

Mathematica

Select[Range[100], IntegerQ[PowerMod[-4, 1/2, #]] &] // Quiet (* After Jean-François Alcover *) (* Robert Price, Apr 19 2025 *)

Sage

def A057129(n) :
    if n%16==0: return False
    for (p, m) in factor(n) :
        if p % 4 not in [1, 2] : return False
    return True
# Eric M. Schmidt, Apr 21 2013