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A259584 Numbers k such that [r[s*k]] - [s[r*k]] = -2, where r = sqrt(2), s=sqrt(3), and [ ] = floor.

%I A259584 #10 Dec 01 2016 16:06:50
%S A259584 116,314,512,657,1340,1422,1620,1818,1900,2161,2243,2441,2639,2982,
%T A259584 3124,3322,3747,3800,3945,4027,4143,4225,4766,5251,5449,5531,5729,
%U A259584 5927,6125,6270,6352,6953,7091,7233,7431,7711,7774,7856,8054,8252,8457,8595,9278,9360
%N A259584 Numbers k such that [r[s*k]] - [s[r*k]] = -2, where r = sqrt(2), s=sqrt(3), and [ ] = floor.
%C A259584 It is easy to prove that [r[s*k]] - [s[r*k]] ranges from -2 to 2. 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.
%C A259584 The first -2 occurs when k = 116.
%H A259584 Clark Kimberling, <a href="/A259584/b259584.txt">Table of n, a(n) for n = 1..10000</a>
%t A259584 z = 12000; r = Sqrt[2]; s = Sqrt[3];
%t A259584 u = Table[Floor[r*Floor[s*n]], {n, 1, z}];
%t A259584 v = Table[Floor[s*Floor[r*n]], {n, 1, z}];
%t A259584 Flatten[Position[u - v, -2]] (* A259584 *)
%t A259584 Take[Flatten[Position[u - v, -1]], 100] (* A259585 *)
%t A259584 Take[Flatten[Position[u - v, 0]], 100]  (* A259725 *)
%t A259584 Take[Flatten[Position[u - v, 1]], 100]  (* A259587 *)
%t A259584 Take[Flatten[Position[u - v, 2]], 100]  (* A259586 *)
%t A259584 Select[Range[10000],Floor[Sqrt[2]Floor[Sqrt[3]#]]-Floor[Sqrt[3]Floor[ Sqrt[ 2]#]]==-2&] (* _Harvey P. Dale_, Dec 01 2016 *)
%Y A259584 Cf. A259585, A259586, A259587, A259724, A259725, A259746.
%K A259584 nonn,easy
%O A259584 1,1
%A A259584 _Clark Kimberling_, Jul 15 2015