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A194379 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(7) and < > denotes fractional part. 4
2, 14, 16, 28, 30, 32, 34, 36, 42, 44, 46, 48, 50, 62, 64, 76, 78, 80, 82, 84, 90, 92, 94, 96, 98, 110, 112, 124, 126, 128, 130, 132, 138, 140, 142, 144, 146, 158, 160, 172, 174, 176, 178, 180, 186, 188, 190, 192, 194, 206, 208, 220, 222, 224, 226, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All the terms are even.  See A194368.

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

r = Sqrt[7]; c = 1/2;

MATHEMATICA

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]]   (* A194378 *)

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

Flatten[Position[t2, 1]]  (* A194379 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];

Flatten[Position[t3, 1]]   (* A194380 *)

CROSSREFS

Cf. A194368.

Sequence in context: A105453 A199368 A121716 * A147832 A022369 A278975

Adjacent sequences:  A194376 A194377 A194378 * A194380 A194381 A194382

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)