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

1,2

Links

Table of n, a(n) for n=1..66.

Example

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.)

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 *)

Crossrefs

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

Sequence in context: A050828 A329405 A194391 * A081534 A373347 A214547

Adjacent sequences: A347465 A347466 A347467 * A347469 A347470 A347471

Keyword

nonn

Author

Clark Kimberling, Oct 28 2021

Status

approved