A194409 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <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

1,1

Comments

Every term is even; see A194368.

Links

Table of n, a(n) for n=1..31.

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 *)

Crossrefs

Cf. A194368.

Sequence in context: A059611 A177085 A338370 * A115166 A050992 A372011

Adjacent sequences: A194406 A194407 A194408 * A194410 A194411 A194412

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved