A194821 a(n) = 1+floor(sum{<((-1)^k)*k*sqrt(2)> : 1<=k<=n}), where < > = fractional part.

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

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