A194413 - OEIS

%I #8 Nov 30 2017 18:22:09

%S 1,3,4,5,7,8,9,11,12,13,14,15,16,17,18,19,20,21,22,23,25,26,27,29,30,

%T 31,33,34,36,37,38,40,41,42,44,45,46,47,48,49,50,51,52,53,54,55,56,57,

%U 61,65,69,70,71,73,74,75,77,78,79,80,81,82,83,84,85,86,87,88,89

%N (A194412)/3.

%C See A194368.

%H G. C. Greubel, <a href="/A194413/b194413.txt">Table of n, a(n) for n = 1..1000</a>

%t r = Sqrt[2]; c = 1/3;

%t x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

%t y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

%t t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t1, 1]]         (* A194411 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];

%t Flatten[Position[t2, 1]]         (* A194412 *)

%t %/3                              (* A194413 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];

%t Flatten[Position[t3, 1]]         (* A194414 *)

%Y Cf. A194368, A194412.

%K nonn

%O 1,2

%A _Clark Kimberling_, Aug 24 2011