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A194822 a(n) = 3+floor( Sum_{k=1..n} <((-1)^k)*k*(1+sqrt(5))/2> ), where < > = fractional part. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The first negative term is a(1291) = -1. - Georg Fischer, Feb 15 2019
LINKS
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A089049 A275235 A029420 * A029405 A339383 A198260
KEYWORD
sign
AUTHOR
Clark Kimberling, Sep 03 2011
EXTENSIONS
Definition corrected by Georg Fischer, Jul 31 2023
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)