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A194396 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(14) and < > denotes fractional part. 4
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 38, 42, 46, 50, 54, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 94, 98, 102, 106, 110, 114, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150 (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..61.

MATHEMATICA

r = Sqrt[14]; 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, 200}];

Flatten[Position[t1, 1]]       (* A194395 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t2, 1]]       (* A194396 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t3, 1]]       (* A194397 *)

CROSSREFS

Cf. A010471, A194368, A194395, A194397.

Sequence in context: A053228 A141098 A084563 * A321193 A284788 A323288

Adjacent sequences:  A194393 A194394 A194395 * A194397 A194398 A194399

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified September 23 12:06 EDT 2021. Contains 347616 sequences. (Running on oeis4.)