A194388 - OEIS

%I #10 Feb 15 2021 02:21:03

%S 2,4,14,16,18,22,24,26,30,32,34,44,46,48,52,54,56,60,62,64,74,76,78,

%T 82,84,86,90,92,94,104,106,108,112,114,116,120,122,124,134,136,138,

%U 142,144,146,150,152,154,164,166,168,172,174,176,180,182,184,194,196

%N Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(11) and < > denotes fractional part.

%C Every term is even; see A194368.

%t r = Sqrt[11]; c = 1/2;

%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]]     (* A194387 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t2, 1]]     (* A194388 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

%t Flatten[Position[t3, 1]]     (* A194389 *)

%Y Cf. A010468, A194368, A194387, A194389.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 23 2011