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A194375 Numbers n such that sum{<1/2+k*r>-<k*r> : 1<=k<=n}>0, where r=sqrt(5) and < > denotes fractional part. 3
1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 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, 70, 71, 73, 74 (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[5]; 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, 500}];

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

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

Flatten[Position[t2, 1]]   (* A194374 *)

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

Flatten[Position[t3, 1]]   (* A194375 *)

CROSSREFS

Cf. A194368.

Sequence in context: A098572 A001955 A184480 * A188222 A329990 A109237

Adjacent sequences:  A194372 A194373 A194374 * A194376 A194377 A194378

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 23 2011

STATUS

approved

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Last modified June 2 16:27 EDT 2020. Contains 334787 sequences. (Running on oeis4.)