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A194414 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(2) and < > denotes fractional part. 5
1, 4, 5, 6, 7, 8, 10, 11, 13, 16, 17, 18, 19, 20, 22, 23, 25, 28, 29, 30, 31, 32, 34, 35, 37, 40, 46, 47, 49, 52, 58, 59, 61, 64, 76, 88, 100, 103, 104, 105, 106, 107, 109, 110, 112, 115, 116, 117, 118, 119, 121, 122, 124, 127, 128, 129, 130, 131, 133, 134 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

MATHEMATICA

r = Sqrt[2]; c = 1/3;

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]]         (* A194411 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];

Flatten[Position[t2, 1]]         (* A194412 *)

%/3                              (* A194413 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];

Flatten[Position[t3, 1]]         (* A194414 *)

CROSSREFS

Cf. A002193, A194368, A194411, A194412, A194413.

Sequence in context: A251392 A076597 A301592 * A182204 A343916 A121541

Adjacent sequences:  A194411 A194412 A194413 * A194415 A194416 A194417

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 23 11:59 EST 2022. Contains 350512 sequences. (Running on oeis4.)