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A194463 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
1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 16, 17, 21, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 37, 38, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A194368.
LINKS
MATHEMATICA
r = GoldenRatio; c = FractionalPart[r/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]] (* A184463 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]] (* A184464 *)
CROSSREFS
Cf. A194368.
Sequence in context: A336654 A004436 A028237 * A140467 A103677 A087919
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved

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Last modified March 3 20:15 EST 2024. Contains 370512 sequences. (Running on oeis4.)