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

5, 7, 10, 11, 14, 15, 17, 19, 20, 21, 22, 28, 30, 33, 34, 37, 38, 40, 42, 43, 44, 45, 51, 53, 56, 57, 60, 61, 63, 65, 66, 67, 68, 74, 76, 79, 80, 83, 84, 86, 88, 89, 90, 91, 97, 99, 102, 103, 106, 107, 109, 111, 112, 113, 114, 120, 122, 125, 126, 129, 130, 132, 134, 135, 136, 137, 143, 145, 148, 149

Offset: 1

Author

N. J. A. Sloane, Nov 29 2016

Keywords

• nonn

Comments

Important for the study of Ramanujan numbers A000594.

References

• 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.

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Crossrefs

Cf. A028736, A000594, A063987, A278580, A028759 (=first 22 terms).

For the primes in this sequence see A191065.

Programs

Mathematica

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 *)

Formula

From Robert Israel, Nov 30 2016: (Start)

a(n+11) = a(n)+23.

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)