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A194416
Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(3) and < > denotes fractional part.
5
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 63, 66, 69, 78, 81, 84, 93, 96, 99, 108, 111, 123, 126, 138, 141, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 216, 219, 222, 231, 234
OFFSET
1,1
COMMENTS
Every term is divisible by 3; see A194368.
MATHEMATICA
r = Sqrt[3]; c = 1/3;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t1, 1]] (* A194415 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]] (* A194416 *)
%/3 (* A194417 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t3, 1]] (* A194418 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved