

A194467


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


1



1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
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OFFSET

1,2


COMMENTS

See A194368.


LINKS

Table of n, a(n) for n=1..69.


MATHEMATICA

Remove["Global`*"];
r = Sqrt[3]; c = 1/r;
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, 200}];
Flatten[Position[t1, 1]] (* A184467 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
Flatten[Position[t3, 1]] (* A184468 *)


CROSSREFS

Cf. A194368.
Sequence in context: A071959 A176845 A196127 * A225857 A168134 A245030
Adjacent sequences: A194464 A194465 A194466 * A194468 A194469 A194470


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 24 2011


STATUS

approved



