

A194418


Numbers n such that sum{<1/3+k*r><k*r> : 1<=k<=n}>0, where r=sqrt(3) and < > denotes fractional part.


5



7, 10, 11, 13, 14, 22, 25, 26, 28, 29, 37, 40, 41, 43, 44, 52, 55, 67, 70, 82, 85, 97, 100, 160, 163, 164, 166, 167, 175, 178, 179, 181, 182, 190, 193, 194, 196, 197, 205, 208, 220, 223, 235, 238, 250, 253, 373, 376, 388, 391, 403, 406
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OFFSET

1,1


COMMENTS

See A194368.


LINKS

Table of n, a(n) for n=1..52.


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

Cf. A194368.
Sequence in context: A060228 A190231 A191875 * A094764 A066468 A088769
Adjacent sequences: A194415 A194416 A194417 * A194419 A194420 A194421


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 24 2011


STATUS

approved



