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A194663 Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part and r = sqrt(2). 4

%I

%S 0,0,2,0,3,0,1,0,4,0,1,0,4,0,0,0,0,0,0,0,0,0,1,0,6,0,1,0,4,0,14,0,14,

%T 0,14,0,11,0,4,0,8,0,18,0,14,0,5,0,10,0,22,0,17,0,6,0,13,0,30,0,31,0,

%U 31,0,31,0,31,0,31,0,25,0,12,0,19,0,37,0,37,0,31,0,22,0,41,0,41

%N Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part and r = sqrt(2).

%H G. C. Greubel, <a href="/A194663/b194663.txt">Table of n, a(n) for n = 1..10000</a>

%t r = Sqrt[2]; z = 13;

%t p[x_] := FractionalPart[x]; f[x_] := Floor[x];

%t w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]

%t Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]

%t TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]

%t s[n_] := Sum[w[n, k], {k, 1, n}] (* A194663 *)

%t Table[s[n], {n, 1, 100}]

%t h[n_, k_] := f[p[n*r] + p[k*r]]

%t Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]] (* A194664 *)

%t TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]

%t t[n_] := Sum[h[n, k], {k, 1, n}]

%t Table[t[n], {n, 1, 100}] (* A194665 *)

%K nonn

%O 1,3

%A _Clark Kimberling_, Sep 01 2011

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Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)