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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 (list; graph; refs; listen; history; text; internal format)
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 A090259

Adjacent sequences:  A194406 A194407 A194408 * A194410 A194411 A194412

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 27 22:38 EST 2022. Contains 350654 sequences. (Running on oeis4.)