cp's OEIS Frontend

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

%I A194663 #8 Feb 02 2018 16:18:23
%S A194663 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 A194663 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 A194663 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 A194663 Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part and r = sqrt(2).
%H A194663 G. C. Greubel, <a href="/A194663/b194663.txt">Table of n, a(n) for n = 1..10000</a>
%t A194663 r = Sqrt[2]; z = 13;
%t A194663 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194663 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194663 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194663 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194663 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194663 *)
%t A194663 Table[s[n], {n, 1, 100}]
%t A194663 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194663 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]    (* A194664 *)
%t A194663 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194663 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194663 Table[t[n], {n, 1, 100}]    (* A194665 *)
%K A194663 nonn
%O A194663 1,3
%A A194663 _Clark Kimberling_, Sep 01 2011