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A194821
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a(n) = 1+floor(sum{<((-1)^k)*k*sqrt(2)> : 1<=k<=n}), where < > = fractional part.
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4
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0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 2, 2, 3, 3
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OFFSET
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1,6
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COMMENTS
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Does 0 occur infinitely many times? Is the sequence unbounded?
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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 = Sqrt[2]; p[x_] := FractionalPart[x];
f[n_] := 1 + Floor[Sum[p[k*r] (-1)^k, {k, 1, n}]]
Table[f[n], {n, 1, 100}] (* A194821 *)
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PROG
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(PARI) for(n=1, 50, print1(1 + floor(sum(k=1, n, (-1)^k*frac(k*sqrt(2))), ", ")) \\ G. C. Greubel, Apr 02 2018
(Magma) [1 + Floor((&+[(-1)^k*(k*Sqrt(2) - Floor(k*Sqrt(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. A194822, A194823, A194824.
Sequence in context: A090464 A277967 A196049 * A044934 A124761 A333925
Adjacent sequences: A194818 A194819 A194820 * A194822 A194823 A194824
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KEYWORD
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nonn
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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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