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 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

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