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A278579 Quadratic non-residues of 23: numbers n such that Jacobi(n,23) = -1.

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%I A278579 #20 Jun 21 2025 14:03:50
%S A278579 5,7,10,11,14,15,17,19,20,21,22,28,30,33,34,37,38,40,42,43,44,45,51,
%T A278579 53,56,57,60,61,63,65,66,67,68,74,76,79,80,83,84,86,88,89,90,91,97,99,
%U A278579 102,103,106,107,109,111,112,113,114,120,122,125,126,129,130,132,134,135,136,137,143,145,148,149
%N A278579 Quadratic non-residues of 23: numbers n such that Jacobi(n,23) = -1.
%C A278579 Important for the study of Ramanujan numbers A000594.
%D A278579 Wilton, John Raymond. "Congruence properties of Ramanujan's function τ(n)." Proceedings of the London Mathematical Society 2.1 (1930): 1-10. See page 1.
%H A278579 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F A278579 From _Robert Israel_, Nov 30 2016: (Start)
%F A278579 a(n+11) = a(n)+23.
%F A278579 G.f.: (x^11+x^10+x^9+x^8+2*x^7+2*x^6+x^5+3*x^4+x^3+3*x^2+2*x+5)/(x^12-x^11-x+1). (End)
%t A278579 LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,1,-1},{5,7,10,11,14,15,17,19,20,21,22,28},80] (* _Harvey P. Dale_, Jan 12 2020 *)
%Y A278579 Cf. A028736, A000594, A063987, A278580, A028759 (=first 22 terms).
%Y A278579 For the primes in this sequence see A191065.
%K A278579 nonn
%O A278579 1,1
%A A278579 _N. J. A. Sloane_, Nov 29 2016