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A194404 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=(1+sqrt(5))/2 and < > denotes fractional part. 5
5, 7, 13, 15, 39, 41, 47, 49, 73, 75, 81, 83, 89, 91, 93, 94, 95, 96, 97, 99, 101, 102, 103, 104, 105, 107, 109, 115, 117, 123, 125, 127, 128, 129, 130, 131, 133, 135, 136, 137, 138, 139, 141, 143, 149, 151, 157, 159, 183, 185, 191, 193, 217, 219, 225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..55.

MATHEMATICA

r = GoldenRatio; 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, 200}];

Flatten[Position[t1, 1]]       (* A194401 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];

Flatten[Position[t2, 1]]       (* A194402 *)

%/2       (* A194403 *)

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

Flatten[Position[t3, 1]]       (* A194404 *)

CROSSREFS

Cf. A001622, A194368, A194401, A194402, A194403.

Sequence in context: A314316 A314317 A314318 * A064465 A314319 A314320

Adjacent sequences:  A194401 A194402 A194403 * A194405 A194406 A194407

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 20 01:01 EST 2022. Contains 350467 sequences. (Running on oeis4.)