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A194382 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(8) and < > denotes fractional part. 5
4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 40, 46, 52, 58, 64, 104, 110, 116, 122, 128, 134, 138, 140, 144, 146, 150, 152, 156, 158, 162, 164, 168, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 204, 208, 210, 214, 216, 220, 222, 226, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..54.

MATHEMATICA

r = Sqrt[8]; 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]]   (* A194381 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t2, 1]]   (* A194382 *)

%/2  (* A194383 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];

Flatten[Position[t3, 1]]   (* A194384 *)

CROSSREFS

Cf. A010466, A194368, A194383.

Sequence in context: A166986 A318487 A047233 * A296655 A310577 A353465

Adjacent sequences:  A194379 A194380 A194381 * A194383 A194384 A194385

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified May 24 18:12 EDT 2022. Contains 354043 sequences. (Running on oeis4.)