cp's OEIS Frontend

A259587 Numbers k such that [r[s*k]] - [s[r*k]] = 2, where r = sqrt(2), s=sqrt(3), and [ ] = floor.

%I A259587 #17 Feb 13 2018 05:58:30
%S A259587 2,3,6,7,9,11,12,14,26,33,36,40,43,48,52,55,59,62,65,72,74,77,82,84,
%T A259587 89,91,93,94,96,101,108,111,115,118,119,122,125,134,137,140,141,144,
%U A259587 147,148,149,151,152,154,159,164,171,175,178,181,188,190,193,194
%N A259587 Numbers k such that [r[s*k]] - [s[r*k]] = 2, where r = sqrt(2), s=sqrt(3), and [ ] = floor.
%C A259587 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; the first appearance of 2 is when k = 41.
%H A259587 G. C. Greubel, <a href="/A259587/b259587.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Clark Kimberling)
%t A259587 z = 12000; r = Sqrt[2]; s = Sqrt[3];
%t A259587 u = Table[Floor[r*Floor[s*n]], {n, 1, z}];
%t A259587 v = Table[Floor[s*Floor[r*n]], {n, 1, z}];
%t A259587 Flatten[Position[u - v, -2]] (* A259584 *)
%t A259587 Take[Flatten[Position[u - v, -1]], 100] (* A259585 *)
%t A259587 Take[Flatten[Position[u - v, 0]], 100]  (* A259725 *)
%t A259587 Take[Flatten[Position[u - v, 1]], 100]  (* A259587 *)
%t A259587 Take[Flatten[Position[u - v, 2]], 100]  (* A259586 *)
%Y A259587 Cf. A259584, A259585, A259586, A259724, A259725, A259746.
%K A259587 nonn,easy
%O A259587 1,1
%A A259587 _Clark Kimberling_, Jul 15 2015