A057126 Numbers n such that 2 is a square mod n.

1, 2, 7, 14, 17, 23, 31, 34, 41, 46, 47, 49, 62, 71, 73, 79, 82, 89, 94, 97, 98, 103, 113, 119, 127, 137, 142, 146, 151, 158, 161, 167, 178, 191, 193, 194, 199, 206, 217, 223, 226, 233, 238, 239, 241, 254, 257, 263, 271, 274, 281, 287, 289, 302, 311, 313, 322

Offset

1,2

Comments

Numbers that are not multiples of 4 and for which all odd prime factors are congruent to +/- 1 mod 8. - Eric M. Schmidt, Apr 20 2013

Apparently the same as the list of numbers primitively represented by the indefinite quadratic form x^2 - 2y^2 (cf. A035251). - N. J. A. Sloane, Jun 11 2014

Links

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

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Maple

with(numtheory); [seq(mroot(2, 2, p), p=1..300)];

Mathematica

ok[n_] := Reduce[ Mod[2 - k^2, n] == 0, k, Integers] =!= False; Prepend[ Select[ Range[400], ok], 1] (* Jean-François Alcover, Sep 20 2012 *)

Prog

(PARI) isok(n) = issquare(Mod(2, n)); \\ Michel Marcus, Feb 19 2016

Crossrefs

Includes the primes in A038873 and these (primes congruent to {1, 2, 7} mod 8) are the prime factors of the terms in this sequence.

Cf. A008784, A057125, A057127, A057128, A057129, A057757, A035251, A038873.

Cf. A087780 (number of solutions mod n).

Sequence in context: A032537 A072120 A247866 * A363026 A319250 A018349

Adjacent sequences: A057123 A057124 A057125 * A057127 A057128 A057129

Keyword

nonn

Author

Henry Bottomley, Aug 10 2000

Extensions

Checked by T. D. Noe, Apr 19 2007

Status

approved