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A194419 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) < 0, where r=sqrt(5) and < > denotes fractional part. 4
4, 5, 8, 59, 76, 77, 80, 131, 148, 149, 152, 203, 220, 221, 224, 275, 292, 293, 296, 686, 758, 830, 902, 974, 991, 992, 995 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..27.

MATHEMATICA

r = Sqrt[5]; 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, 1000}];

Flatten[Position[t1, 1]]         (* A194419 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];

Flatten[Position[t2, 1]]         (* A194420 *)

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

Flatten[Position[t3, 1]]         (* A194421 *)

CROSSREFS

Cf. A194368.

Sequence in context: A229861 A140315 A055497 * A175380 A263151 A093088

Adjacent sequences:  A194416 A194417 A194418 * A194420 A194421 A194422

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)