A028736 Nonsquares mod 23.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

Examples

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

References

• 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

Links

• George E. Andrews, James A. Sellers, Congruences for the Fishburn Numbers, arXiv preprint arXiv:1401.5345 [math.NT], 2014.

Crossrefs

Cf. A010385, A028759, A278579.

Programs

Mathematica

Select[Range[22], JacobiSymbol[#, 23] != 1 &] (* Jean-François Alcover, Oct 07 2018 *)

Scala

val squaresMod23 = (0 to 22).map(n => n * n).map(_ % 23)
(0 to 22).diff(squaresMod23) // Alonso del Arte, Nov 23 2019