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A194406 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - ) = 0 where < > denotes fractional part.

%I A194406 #9 Feb 15 2021 22:33:03
%S A194406 2,4,6,8,12,26,30,32,34,36,38,40,44,58,62,64,66,68,70,74,78,80,82,84,
%T A194406 86,90,94,96,98,100,102,106,110,112,114,116,118,122,126,128,130,132,
%U A194406 134,138,152,156,158,160,162,164,166,170,184,188,190,192,194,196
%N A194406 Numbers m such that Sum_{k=1..m} (<1/2 + k*e> - <k*e>) = 0 where < > denotes fractional part.
%C A194406 Every term is even; see A194368.
%t A194406 r = E; c = 1/2;
%t A194406 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194406 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194406 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194406 Flatten[Position[t1, 1]]       (* A194405 *)
%t A194406 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194406 Flatten[Position[t2, 1]]       (* A194406 *)
%t A194406 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194406 Flatten[Position[t3, 1]]       (* A194407 *)
%Y A194406 Cf. A194368.
%K A194406 nonn
%O A194406 1,1
%A A194406 _Clark Kimberling_, Aug 24 2011