

A194676


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


4



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, 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, 45, 53, 17, 17, 4, 1, 12, 60, 19, 3, 20, 20, 50, 5, 48, 22, 47, 66, 0, 75, 73, 27, 25
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OFFSET

1,4


LINKS

Table of n, a(n) for n=1..79.


MATHEMATICA

r = E; z = 15;
p[x_] := FractionalPart[x]; f[x_] := Floor[x];
w[n_, k_] := p[r^n] + p[r^k]  p[r^n + r^k]
Flatten[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
(* A194675 *)
TableForm[Table[w[n, k], {n, 1, z}, {k, 1, n}]]
s[n_] := Sum[w[n, k], {k, 1, n}] (* A194676 *)
Table[s[n], {n, 1, 100}]
h[n_, k_] := f[p[n*r] + p[k*r]]
Flatten[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
(* A194677 *)
TableForm[Table[h[n, k], {n, 1, z}, {k, 1, n}]]
t[n_] := Sum[h[n, k], {k, 1, n}]
Table[t[n], {n, 1, 100}] (* A194678 *)


CROSSREFS

Cf. A194675.
Sequence in context: A064943 A081478 A105341 * A151694 A298745 A323860
Adjacent sequences: A194673 A194674 A194675 * A194677 A194678 A194679


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 01 2011


STATUS

approved



