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

%I A347468 #4 Nov 20 2021 21:25:16
%S A347468 1,3,5,7,9,11,13,14,15,17,18,19,21,22,23,24,25,26,27,28,29,31,32,33,
%T A347468 35,36,38,39,40,42,43,44,45,46,48,49,50,52,53,54,56,57,58,60,62,64,66,
%U A347468 68,70,72,74,76,78,80,81,82,84,85,86,88,89,90,92,93,94,95
%N A347468 Numbers k such that floor(k*sqrt(3)) = floor(h*sqrt(2)) for some h.
%e A347468 Beatty sequence for sqrt(2): (1,2,4,5,7,8,9,11,12,14,...)
%e A347468 Beatty sequence for sqrt(3): (1,3,5,6,8,10,12,13,15,...)
%e A347468 Intersection: (1,5,8,12,...), as in A346308.
%e A347468 a(2) = 3 because floor(3*sqrt(3)) = floor(4*sqrt(2)).  (For each such k, there is only one such h.)
%t A347468 z = 200; r = Sqrt[2]; s = Sqrt[3];
%t A347468 u = Table[Floor[n r], {n, 0, z}]; (*A001951*)
%t A347468 v = Table[Floor[n s], {n, 1, z}]; (*A022838*)
%t A347468 w = Intersection[u, v]  (*A346308*)
%t A347468 zz = -1 + Length[w];
%t A347468 Table[Ceiling[w[[n]]/r], {n, 1, zz}] (* A347467 *)
%t A347468 Table[Ceiling[w[[n]]/s], {n, 1, zz}] (* A347468 *)
%Y A347468 Cf. A001951, A022838, A346308, A347467, A347469.
%K A347468 nonn
%O A347468 1,2
%A A347468 _Clark Kimberling_, Oct 28 2021