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A194461 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=(1+sqrt(5))/2 and c=(-1+sqrt(5))/4, and < > denotes fractional part. 1
3, 6, 8, 9, 11, 12, 16, 19, 21, 22, 24, 25, 29, 32, 42, 45, 55, 58, 61, 63, 64, 66, 67, 71, 74, 76, 77, 79, 80, 84, 87, 97, 100, 110, 113, 116, 118, 119, 121, 122, 126, 129, 131, 132, 134, 135, 139, 142, 144, 145, 147, 148, 150, 151, 152, 153, 154, 155, 156 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..59.

MATHEMATICA

r = GoldenRatio; c = (1/2) FractionalPart[r];

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]]  (* A184461 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t3, 1]]  (* A184462 *)

CROSSREFS

Cf. A194368.

Sequence in context: A190234 A036558 A005870 * A186385 A335155 A231005

Adjacent sequences:  A194458 A194459 A194460 * A194462 A194463 A194464

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified June 17 16:49 EDT 2021. Contains 345085 sequences. (Running on oeis4.)