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 A194401 Numbers n such that sum{<1/2+k*r>- : 1<=k<=n}<0, where r=(1+sqrt(5))/2 and < > denotes fractional part. 5
 1, 3, 9, 11, 17, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 43, 45, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 71, 77, 79, 85, 87, 111, 113, 119, 121, 145, 147, 153, 155, 161, 163, 165, 166, 167, 168, 169, 171, 173, 174, 175, 176, 177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 Cf. A194368. Sequence in context: A131861 A131859 A096187 * A190238 A047471 A201544 Adjacent sequences:  A194398 A194399 A194400 * A194402 A194403 A194404 KEYWORD nonn AUTHOR Clark Kimberling, Aug 24 2011 STATUS approved

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