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A194666 Number of k in [1,n] for which <r^n>+<r^k> > 1, where < > = fractional part and r = sqrt(3). 4
1, 0, 0, 0, 2, 0, 3, 0, 2, 0, 6, 0, 5, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 13, 0, 11, 0, 8, 0, 16, 0, 17, 0, 15, 0, 19, 0, 16, 0, 18, 0, 21, 0, 7, 0, 15, 0, 9, 0, 21, 0, 27, 0, 28, 0, 27, 0, 19, 0, 11, 0, 24, 0, 29, 0, 9, 0, 23, 0, 18, 0, 6, 0, 16, 0, 39, 0, 39, 0, 32, 0, 2, 0, 6, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..86.

MATHEMATICA

r = Sqrt[3]; z = 13;

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}]]

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

s[n_] := Sum[w[n, k], {k, 1, n}]  (* A194666 *)

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}]]

  (* A194667 *)

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}]   (* A194668 *)

CROSSREFS

Sequence in context: A128143 A292561 A027640 * A325799 A229946 A127460

Adjacent sequences:  A194663 A194664 A194665 * A194667 A194668 A194669

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 01 2011

STATUS

approved

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Last modified August 4 15:25 EDT 2021. Contains 346447 sequences. (Running on oeis4.)