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A194822
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a(n) = 3+floor(sum{<((-1)^k)*k*sqrt(3)> : 1<=k<=n}), where < > = fractional part.
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4
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2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 1, 2, 2
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OFFSET
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1,1
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COMMENTS
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The first negative term is a(1291) = -1. - Georg Fischer, Feb 15 2019
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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r = GoldenRatio; p[x_] := FractionalPart[x];
f[n_] := 3 + Floor[Sum[p[k*r] (-1)^k, {k, 1, n}]]
Table[f[n], {n, 1, 100}] (* A194822 *)
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PROG
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(PARI) for(n=1, 50, print1(3 + floor(sum(k=1, n, (-1)^k*frac(k*(1+sqrt(5))/2)), ", ")) \\ G. C. Greubel, Apr 02 2018
(Magma) [3 + Floor((&+[(-1)^k*(k*(1+Sqrt(5))/2 - Floor(k*(1+Sqrt(5))/2)) :k in [1..n]])) : n in [1..50]]; // G. C. Greubel, Apr 02 2018
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CROSSREFS
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Cf. A194821, A194823, A194824.
Sequence in context: A089049 A275235 A029420 * A029405 A339383 A198260
Adjacent sequences: A194819 A194820 A194821 * A194823 A194824 A194825
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KEYWORD
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sign
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AUTHOR
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Clark Kimberling, Sep 03 2011
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STATUS
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approved
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