A347468 Numbers k such that floor(k*sqrt(3)) = floor(h*sqrt(2)) for some h.

1, 3, 5, 7, 9, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 85, 86, 88, 89, 90, 92, 93, 94, 95

Offset: 1

Author

Clark Kimberling, Oct 28 2021

Keywords

• nonn

Examples

			Beatty sequence for sqrt(2): (1,2,4,5,7,8,9,11,12,14,...)
Beatty sequence for sqrt(3): (1,3,5,6,8,10,12,13,15,...)
Intersection: (1,5,8,12,...), as in A346308.
a(2) = 3 because floor(3*sqrt(3)) = floor(4*sqrt(2)).  (For each such k, there is only one such h.)
		

Crossrefs

Cf. A001951, A022838, A346308, A347467, A347469.

Programs

Mathematica

z = 200; r = Sqrt[2]; s = Sqrt[3];
u = Table[Floor[n r], {n, 0, z}]; (*A001951*)
v = Table[Floor[n s], {n, 1, z}]; (*A022838*)
w = Intersection[u, v]  (*A346308*)
zz = -1 + Length[w];
Table[Ceiling[w[[n]]/r], {n, 1, zz}] (* A347467 *)
Table[Ceiling[w[[n]]/s], {n, 1, zz}] (* A347468 *)