

A194198


[sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(10).


2



0, 0, 0, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 15, 16, 16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35, 36
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OFFSET

1,5


LINKS



FORMULA

a(n) ~ n/2 by Weyl's equidistribution theorem.  Robert Israel, Jul 17 2019


MAPLE

map(floor, ListTools:PartialSums([seq(frac(k*sqrt(10)), k=1..100)])); # Robert Israel, Jul 17 2019


MATHEMATICA

r = Sqrt[10];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194198 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194199 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



