A194409 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=Pi and < > denotes fractional part.

6, 8, 12, 16, 18, 24, 88, 94, 96, 100, 104, 106, 112, 114, 118, 122, 124, 130, 208, 214, 216, 220, 224, 228, 230, 236, 328, 334, 336, 342, 448

Offset: 1

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

Every term is even; see A194368.

Crossrefs

Cf. A194368.

Programs

Mathematica

r = Pi; 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]]         (* A194408 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 1500}];
Flatten[Position[t2, 1]]         (* A194409 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 1500}];
Flatten[Position[t3, 1]]         (* A194410 *)