A057126 - OEIS

%I #24 May 07 2020 10:46:36

%S 1,2,7,14,17,23,31,34,41,46,47,49,62,71,73,79,82,89,94,97,98,103,113,

%T 119,127,137,142,146,151,158,161,167,178,191,193,194,199,206,217,223,

%U 226,233,238,239,241,254,257,263,271,274,281,287,289,302,311,313,322

%N Numbers n such that 2 is a square mod n.

%C 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

%C 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

%H T. D. Noe, <a href="/A057126/b057126.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

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

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

%o (PARI) isok(n) = issquare(Mod(2,n)); \\ _Michel Marcus_, Feb 19 2016

%Y 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.

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

%Y Cf. A087780 (number of solutions mod n).

%K nonn

%O 1,2

%A _Henry Bottomley_, Aug 10 2000

%E Checked by _T. D. Noe_, Apr 19 2007