A194823 a(n) = 2+floor(sum{<((-1)^k)*k*e> : 1<=k<=n}), where < > = fractional part.

1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2

Offset

1,4

Links

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

Mathematica

r = E; p[x_] := FractionalPart[x];
f[n_] := 2 + Floor[Sum[p[k*r] (-1)^k, {k, 1, n}]]
Table[f[n], {n, 1, 1020}]   (* A194823 *)

Prog

(PARI) for(n=1, 50, print1(2 + floor(sum(k=1, n, (-1)^k*frac(k*exp(1))), ", ")) \\ G. C. Greubel, Apr 02 2018
(Magma) [2 + Floor((&+[(-1)^k*(k*Exp(1) - Floor(k*Exp(1))) :k in [1..n]])) : n in [1..50]]; // G. C. Greubel, Apr 02 2018

Crossrefs

Cf. A194821, A194822, A194824.

Sequence in context: A233544 A026535 A080462 * A098396 A297773 A043532

Adjacent sequences: A194820 A194821 A194822 * A194824 A194825 A194826

Keyword

nonn

Author

Clark Kimberling, Sep 03 2011

Status

approved