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Numbers k such that {rk} > c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.
3

%I #8 Apr 21 2021 03:47:18

%S 1,4,5,7,8,11,14,15,18,21,22,24,25,28,29,31,32,35,38,39,41,42,45,46,

%T 48,49,52,55,56,59,62,63,65,66,69,72,73,76,79,80,82,83,86,87,89,90,93,

%U 96,97,100,103,104,106,107,110,113,114,117,120,121,123,124,127,128,130,131

%N Numbers k such that {rk} > c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.

%C Positions of 1 in A083035.

%e (See A120243.)

%t r = Sqrt[1/2]; b = 2; c = 0;

%t f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];

%t t = Table[f[n], {n, 1, 200}] (* A083035 *)

%t Flatten[Position[t, 0]] (* A120752 *)

%t Flatten[Position[t, 1]] (* A120753 *)

%Y Cf. A083035, A120752, A190762.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jul 01 2006