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

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, 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, 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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Mathematica

r = Sqrt[2]; 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}]  (* A194663 *)
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}]]    (* A194664 *)
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}]    (* A194665 *)

Crossrefs

Sequence in context: A341980 A218031 A135523 * A135685 A349447 A164658

Adjacent sequences: A194660 A194661 A194662 * A194664 A194665 A194666

Keyword

nonn

Author

Clark Kimberling, Sep 01 2011

Status

approved