A259585 Numbers k such that [r[s*k]] - [s[r*k]] = -1, where r = sqrt(2), s=sqrt(3), and [ ] = floor.

5, 8, 15, 29, 34, 39, 42, 45, 46, 49, 56, 58, 68, 71, 75, 87, 92, 95, 99, 102, 105, 109, 112, 121, 124, 127, 128, 131, 145, 150, 157, 162, 169, 174, 177, 184, 187, 191, 198, 203, 206, 213, 232, 237, 240, 243, 244, 247, 254, 256, 266, 269, 273, 285, 290, 295

Offset: 1

Author

Clark Kimberling, Jul 15 2015

Keywords

• nonn
• easy

Comments

It is easy to prove that [r[s*k]] - [s[r*k]] ranges from -2 to 2.

Examples

			For k = 1 to 10, the values of [r[s*k]] - [s[r*k]] are 0, 1, 1, 0, -1, 1, 1, -1, 1, 0, so that a(1) = 5.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Clark Kimberling)

Crossrefs

Cf. A259584, A259586, A259587, A259724, A259725, A259746.

Programs

Mathematica

z = 12000; r = Sqrt[2]; s = Sqrt[3];
u = Table[Floor[r*Floor[s*n]], {n, 1, z}];
v = Table[Floor[s*Floor[r*n]], {n, 1, z}];
Flatten[Position[u - v, -2]] (* A259584 *)
Take[Flatten[Position[u - v, -1]], 100] (* A259585 *)
Take[Flatten[Position[u - v, 0]], 100]  (* A259725 *)
Take[Flatten[Position[u - v, 1]], 100]  (* A259587 *)
Take[Flatten[Position[u - v, 2]], 100]  (* A259586 *)