A347467 Numbers h such that floor(k*sqrt(3)) = floor(h*sqrt(2)) for some k.

1, 4, 6, 9, 11, 14, 16, 17, 18, 21, 22, 23, 26, 27, 28, 29, 31, 32, 33, 34, 36, 38, 39, 41, 43, 44, 46, 48, 49, 51, 53, 54, 55, 56, 59, 60, 61, 64, 65, 66, 68, 70, 71, 73, 76, 78, 81, 83, 86, 88, 91, 93, 96, 98, 99, 101, 103, 104, 105, 108, 109, 110, 113

Offset

1,2

Links

Table of n, a(n) for n=1..63.

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) = 4 because floor(3*sqrt(3)) = floor(4*sqrt(2)).  (For each such h, there is only one such k.)

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, A347468, A347469.

Sequence in context: A234373 A189756 A133578 * A285078 A186318 A186345

Adjacent sequences: A347464 A347465 A347466 * A347468 A347469 A347470

Keyword

nonn

Author

Clark Kimberling, Oct 16 2021

Status

approved