

A194425


Numbers m such that Sum_{k=1..m} (<2/3 + k*r>  <k*r>) > 0, where r=sqrt(2) and < > denotes fractional part.


5



5, 8, 10, 11, 17, 20, 22, 23, 29, 32, 34, 35, 37, 38, 39, 40, 41, 44, 46, 47, 49, 50, 51, 52, 53, 56, 58, 59, 61, 62, 63, 64, 65, 68, 80, 92, 104, 107, 109, 110, 116, 119, 121, 122, 128, 131, 133, 134, 136, 137, 138, 139, 140, 143, 145, 146, 148, 149, 150
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OFFSET

1,1


COMMENTS



LINKS



MATHEMATICA

r = Sqrt[2]; c = 2/3;
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, 300}];
Flatten[Position[t1, 1]] (* A194422 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]] (* A194423 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]] (* A194425 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



