A194371 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(3) and fractional part is denoted by < >.

1, 5, 9, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 31, 35, 39, 57, 61, 65, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 87, 91, 95, 113, 117, 121, 125, 127, 128, 129, 131, 132, 133, 135, 136, 137, 139, 143, 147, 151, 169, 173, 177, 181, 183, 184, 185, 187

Offset: 1

Author

Clark Kimberling, Aug 23 2011

Keywords

• nonn

Comments

See A194368.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A194368.

Programs

Mathematica

r = Sqrt[3]; c = 1/2;
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, 100}];
Flatten[Position[t1, 1]]  (* A194371 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194372 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194373 *)