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%I #11 Sep 08 2022 08:45:58
%S 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,
%T 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,
%U 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
%N a(n) = 1+floor(sum{<((-1)^k)*k*sqrt(2)> : 1<=k<=n}), where < > = fractional part.
%C Does 0 occur infinitely many times? Is the sequence unbounded?
%H G. C. Greubel, <a href="/A194821/b194821.txt">Table of n, a(n) for n = 1..10000</a>
%t r = Sqrt[2]; p[x_] := FractionalPart[x];
%t f[n_] := 1 + Floor[Sum[p[k*r] (-1)^k, {k, 1, n}]]
%t Table[f[n], {n, 1, 100}] (* A194821 *)
%o (PARI) for(n=1,50, print1(1 + floor(sum(k=1,n, (-1)^k*frac(k*sqrt(2))), ", ")) \\ _G. C. Greubel_, Apr 02 2018
%o (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
%Y Cf. A194822, A194823, A194824.
%K nonn
%O 1,6
%A _Clark Kimberling_, Sep 03 2011
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