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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)