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A194821 a(n) = 1+floor(sum{<((-1)^k)*k*sqrt(2)> : 1<=k<=n}), where < > = fractional part. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Does 0 occur infinitely many times?  Is the sequence unbounded?

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A194822, A194823, A194824.

Sequence in context: A090464 A277967 A196049 * A044934 A124761 A333925

Adjacent sequences:  A194818 A194819 A194820 * A194822 A194823 A194824

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 03 2011

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)