A380818 Numbers k such that the Diophantine equation d_r*x^r + ... + d_0*x^0 = 0 has an integer solution. k = (d_r .. d_0) in decimal notation, d_i are the digits of k.

0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, 33, 36, 39, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 110, 120, 121, 130, 132, 140, 143, 144, 150, 154, 156, 160, 165, 168, 169, 170, 176, 180, 187, 190, 198, 200, 210, 220, 230, 231, 240, 242, 250

Offset: 1

Author

Ctibor O. Zizka, Feb 04 2025

Keywords

• nonn
• base

Comments

For r >= 1, d_r >= 1, numbers k = d_r*10^r are terms. It looks like the solution x (if it exists) is from [-9, 0].

Examples

			k = 68: the Diophantine equation 6*x + 8 = 0 has no integer solution, thus k = 68 is not a term.
k = 132: the Diophantine equation 1*x^2 + 3*x + 2 = 0 has integer solutions x = -1, x = -2, thus k = 132 is a term.
		

Crossrefs

Cf. A037124 (for k >= 10).