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A194402 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. 6
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 26, 28, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 60, 62, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 98, 100, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 132, 134, 140, 142, 144, 146, 148, 150, 152, 154 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Every term is even; see A194368 and A194403.
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: A234521 A085125 A251237 * A134930 A084562 A344453
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved

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Last modified June 22 21:50 EDT 2024. Contains 373610 sequences. (Running on oeis4.)