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A194370 Numbers n such that sum{<1/2+k*r>-<k*r> : 1<=k<=n}>0, where r=sqrt(2) and < > denotes fractional part. 3
1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 18, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 73, 75, 76, 77, 78, 79, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..69.

MATHEMATICA

r = Sqrt[2]; 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]]  (* empty *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];

Flatten[Position[t2, 1]] (* A194368 *)

%/2 (* A194369 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];

Flatten[Position[t3, 1]] (* A194370 *)

CROSSREFS

Cf. A194368.

Sequence in context: A039175 A048293 A039129 * A039092 A289178 A212450

Adjacent sequences:  A194367 A194368 A194369 * A194371 A194372 A194373

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified June 2 07:15 EDT 2020. Contains 334767 sequences. (Running on oeis4.)