A106311 Possible positive values of the discriminant of irreducible monic integral cubic polynomials.

49, 81, 148, 169, 229, 257, 316, 321, 361, 404, 469, 473, 564, 568, 592, 621, 697, 729, 733, 756, 761, 785, 788, 837, 892, 916, 940, 985, 993, 1016, 1076, 1101, 1129, 1229, 1257, 1264, 1300, 1304, 1345, 1369, 1373, 1384, 1396, 1425, 1436, 1489, 1492, 1509

Offset: 1

Author

T. D. Noe, May 17 2005

Keywords

• nonn

Comments

These discriminants were found by examining all irreducible integral cubic polynomials x^3+ax^2+bx+c for a,b,c in [ -30,30]. Closely related to A006832, discriminants of totally real cubic fields.

Links

• Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
• Eric Weisstein's World of Mathematics, Polynomial Discriminant