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A194462
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Numbers n such that sum{<c+k*r>-<k*r> : 1<=k<=n}>0, where r=(1+sqrt(5))/2 and c=(-1+sqrt(5))/4, and < > denotes fractional part.
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1
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1, 2, 4, 5, 7, 10, 13, 14, 15, 17, 18, 20, 23, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 60, 62, 65, 68, 69, 70, 72, 73, 75, 78, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 101
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OFFSET
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1,2
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COMMENTS
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See A194368.
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LINKS
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Table of n, a(n) for n=1..68.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A194368.
Sequence in context: A058212 A007997 A123120 * A163267 A036559 A083022
Adjacent sequences: A194459 A194460 A194461 * A194463 A194464 A194465
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Aug 24 2011
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STATUS
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approved
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