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Nonsquares mod 23.
3

%I #27 Nov 24 2019 00:02:01

%S 5,7,10,11,14,15,17,19,20,21,22

%N Nonsquares mod 23.

%D Srinivasa Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962. See "Congruence properties of partitions", p. 230. - _N. J. A. Sloane_, Jun 01 2014

%H George E. Andrews, James A. Sellers, <a href="http://arxiv.org/abs/1401.5345">Congruences for the Fishburn Numbers</a>, arXiv preprint arXiv:1401.5345 [math.NT], 2014.

%e Since 11 is not a perfect square and there are no solutions to x^2 = 11 mod 23, 11 is in the sequence.

%e Although 12 is not a perfect square either, there are solutions to x^2 = 12 mod 23, such as x = 9, x = 14. Thus 12 is not in the sequence.

%t Select[Range[22], JacobiSymbol[#, 23] != 1 &] (* _Jean-François Alcover_, Oct 07 2018 *)

%o (Scala) val squaresMod23 = (0 to 22).map(n => n * n).map(_ % 23)

%o (0 to 22).diff(squaresMod23) // _Alonso del Arte_, Nov 23 2019

%Y Cf. A010385, A028759, A278579.

%K nonn,fini,full

%O 1,1

%A _N. J. A. Sloane_