A194372 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(3) and < > denotes fractional part.

2, 4, 6, 8, 10, 12, 14, 18, 22, 26, 28, 30, 32, 34, 36, 38, 40, 42, 46, 50, 54, 56, 58, 60, 62, 64, 66, 68, 70, 74, 78, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 106, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 134, 138, 140, 142, 144, 146, 148, 150, 152

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, A194371.

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 *)