cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A194676 Number of k in [1,n] for which + > 1, where < > = fractional part.

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%I A194676 #5 Mar 30 2012 18:57:43
%S A194676 1,1,0,2,2,2,6,8,1,4,1,9,4,3,4,6,14,1,19,7,8,2,4,19,7,21,22,10,2,10,
%T A194676 10,24,2,30,27,7,11,7,38,14,8,13,14,37,0,4,12,15,3,15,4,35,38,15,26,5,
%U A194676 45,53,17,17,4,1,12,60,19,3,20,20,50,5,48,22,47,66,0,75,73,27,25
%N A194676 Number of k in [1,n] for which <e^n>+<e^k> > 1, where < > = fractional part.
%t A194676 r = E; z = 15;
%t A194676 p[x_] := FractionalPart[x]; f[x_] := Floor[x];
%t A194676 w[n_, k_] := p[r^n] + p[r^k] - p[r^n + r^k]
%t A194676 Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194676  (* A194675 *)
%t A194676 TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
%t A194676 s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194676 *)
%t A194676 Table[s[n], {n, 1, 100}]
%t A194676 h[n_, k_] := f[p[n*r] + p[k*r]]
%t A194676 Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194676   (* A194677 *)
%t A194676 TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
%t A194676 t[n_] := Sum[h[n, k], {k, 1, n}]
%t A194676 Table[t[n], {n, 1, 100}]  (* A194678 *)
%Y A194676 Cf. A194675.
%K A194676 nonn
%O A194676 1,4
%A A194676 _Clark Kimberling_, Sep 01 2011