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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
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
Sequence in context: A314316 A314317 A314318 * A064465 A314319 A314320
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved

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Last modified June 14 15:00 EDT 2024. Contains 373400 sequences. (Running on oeis4.)