login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057125 Numbers n such that 3 is a square mod n. 12
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 (list; graph; refs; listen; history; text; internal format)
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 A294510

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 13:05 EST 2021. Contains 349563 sequences. (Running on oeis4.)