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A259585 Numbers k such that [r[s*k]] - [s[r*k]] = -1, where r = sqrt(2), s=sqrt(3), and [ ] = floor.

%I A259585 #16 Feb 13 2018 05:58:38
%S A259585 5,8,15,29,34,39,42,45,46,49,56,58,68,71,75,87,92,95,99,102,105,109,
%T A259585 112,121,124,127,128,131,145,150,157,162,169,174,177,184,187,191,198,
%U A259585 203,206,213,232,237,240,243,244,247,254,256,266,269,273,285,290,295
%N A259585 Numbers k such that [r[s*k]] - [s[r*k]] = -1, where r = sqrt(2), s=sqrt(3), and [ ] = floor.
%C A259585 It is easy to prove that [r[s*k]] - [s[r*k]] ranges from -2 to 2.
%H A259585 G. C. Greubel, <a href="/A259585/b259585.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Clark Kimberling)
%e A259585 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, so that a(1) = 5.
%t A259585 z = 12000; r = Sqrt[2]; s = Sqrt[3];
%t A259585 u = Table[Floor[r*Floor[s*n]], {n, 1, z}];
%t A259585 v = Table[Floor[s*Floor[r*n]], {n, 1, z}];
%t A259585 Flatten[Position[u - v, -2]] (* A259584 *)
%t A259585 Take[Flatten[Position[u - v, -1]], 100] (* A259585 *)
%t A259585 Take[Flatten[Position[u - v, 0]], 100]  (* A259725 *)
%t A259585 Take[Flatten[Position[u - v, 1]], 100]  (* A259587 *)
%t A259585 Take[Flatten[Position[u - v, 2]], 100]  (* A259586 *)
%Y A259585 Cf. A259584, A259586, A259587, A259724, A259725, A259746.
%K A259585 nonn,easy
%O A259585 1,1
%A A259585 _Clark Kimberling_, Jul 15 2015