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A194409
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=Pi and < > denotes fractional part.
4
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.
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved