A057125 Numbers n such that 3 is a square mod n.

1, 2, 3, 6, 11, 13, 22, 23, 26, 33, 37, 39, 46, 47, 59, 61, 66, 69, 71, 73, 74, 78, 83, 94, 97, 107, 109, 111, 118, 121, 122, 131, 138, 141, 142, 143, 146, 157, 166, 167, 169, 177, 179, 181, 183, 191, 193, 194, 213, 214, 218, 219, 222, 227, 229, 239, 241, 242

Offset

1,2

Comments

Numbers that are not multiples of 4 or 9 and for which all prime factors greater than 3 are congruent to +/- 1 mod 12. - Eric M. Schmidt, Apr 21 2013

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Example

3^2==3 (mod 6), so 6 is a member.

Maple

# Beware: Since 2007 at least and up to Maple 16 at least, the following Maple code returns the wrong answer for n = 6:
with(numtheory): [seq(`if`(mroot(3, 2, n)=FAIL, NULL, n), n=1..400)];
# second Maple program:
with(numtheory): mroot(3, 2, 6):=3:
a:= proc(n) option remember; local m;
      for m from 1+`if`(n=1, 0, a(n-1))
      while mroot(3, 2, m)=FAIL do od; m
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Feb 24 2017

Mathematica

Prepend[ Select[ Range[300], Reduce[Mod[3 - k^2, #] == 0, k, Integers] =!= False &], 1]  (* Jean-François Alcover, Sep 20 2012 *)

Prog

(PARI) isok(n) = issquare(Mod(3, n)); \\ Michel Marcus, Feb 19 2016
(Magma) [n: n in [1..300] | exists(t){x : x in ResidueClassRing(n) | x^2 eq 3}]; // Vincenzo Librandi, Feb 20 2016

Crossrefs

Includes the primes in A038874 and these (primes congruent to {1, 2, 3, 11} mod 12) are the prime factors of the terms in this sequence. Cf. A008784, A057126, A057127, A057128, A057129.

Cf. A057759.

Sequence in context: A124593 A125882 A057758 * A018687 A337172 A361103

Adjacent sequences: A057122 A057123 A057124 * A057126 A057127 A057128

Keyword

nonn

Author

Henry Bottomley, Aug 10 2000

Extensions

Edited by N. J. A. Sloane, Oct 25 2008 at the suggestion of R. J. Mathar.

Status

approved