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.

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A194742 Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part.

Original entry on oeis.org

1, 2, 3, 4, 1, 3, 5, 7, 1, 4, 7, 10, 1, 5, 9, 13, 1, 6, 11, 16, 21, 5, 11, 17, 23, 4, 11, 18, 25, 3, 11, 19, 27, 2, 11, 20, 29, 38, 9, 19, 29, 39, 7, 18, 29, 40, 5, 17, 29, 41, 3, 16, 29, 42, 55, 13, 27, 41, 55, 10, 25, 40, 55, 7, 23, 39, 55, 4, 21, 38, 55, 72, 17, 35, 53
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194743, A194738.

Programs

  • Mathematica
    r = Sqrt[5]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194742 *)
Table[t[n], {n, 1, 100}]   (* A194743 *)

A194743 Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.

Original entry on oeis.org

0, 0, 0, 0, 4, 3, 2, 1, 8, 6, 4, 2, 12, 9, 6, 3, 16, 12, 8, 4, 0, 17, 12, 7, 2, 22, 16, 10, 4, 27, 20, 13, 6, 32, 24, 16, 8, 0, 30, 21, 12, 3, 36, 26, 16, 6, 42, 31, 20, 9, 48, 36, 24, 12, 0, 43, 30, 17, 4, 50, 36, 22, 8, 57, 42, 27, 12, 64, 48, 32, 16, 0, 56, 39, 22, 5, 64
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194743, A194738.

Programs

  • Mathematica
    r = Sqrt[5]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194742 *)
Table[t[n], {n, 1, 100}]   (* A194743 *)

A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part.

Original entry on oeis.org

1, 1, 1, 1, 5, 4, 3, 2, 9, 7, 5, 3, 13, 10, 7, 4, 17, 13, 9, 5, 1, 18, 13, 8, 3, 23, 17, 11, 5, 28, 21, 14, 7, 33, 25, 17, 9, 1, 31, 22, 13, 4, 37, 27, 17, 7, 43, 32, 21, 10, 49, 37, 25, 13, 1, 44, 31, 18, 5, 51, 37, 23, 9, 58, 43, 28, 13, 65, 49, 33, 17, 1, 57, 40, 23, 6
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194745, A194738.

Programs

  • Mathematica
    r = -Sqrt[5]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194744 *)
Table[t[n], {n, 1, 100}]   (* A194745 *)

A194745 Number of k such that {-k*sqrt(5)} > {-n*sqrt(5)}, where { } = fractional part.

Original entry on oeis.org

0, 1, 2, 3, 0, 2, 4, 6, 0, 3, 6, 9, 0, 4, 8, 12, 0, 5, 10, 15, 20, 4, 10, 16, 22, 3, 10, 17, 24, 2, 10, 18, 26, 1, 10, 19, 28, 37, 8, 18, 28, 38, 6, 17, 28, 39, 4, 16, 28, 40, 2, 15, 28, 41, 54, 12, 26, 40, 54, 9, 24, 39, 54, 6, 22, 38, 54, 3, 20, 37, 54, 71, 16, 34, 52, 70
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194744, A194738.

Programs

  • Mathematica
    r = -Sqrt[5]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194744 *)
Table[t[n], {n, 1, 100}]   (* A194745 *)

A194746 Number of k such that {k*sqrt(6)} < {n*sqrt(6)}, where { } = fractional part.

Original entry on oeis.org

1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 11, 5, 11, 4, 11, 3, 11, 2, 11, 20, 9, 19, 7, 18, 5, 17, 3, 16, 1, 15, 29, 12, 27, 9, 25, 6, 23, 3, 21, 39, 17, 36, 13, 33, 9, 30, 5, 27, 1, 24, 47, 19, 43, 14, 39, 9, 35, 4, 31, 58, 25, 53, 19, 48, 13, 43, 7, 38, 1, 33, 65, 26, 59, 19, 53, 12
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194747, A194738.

Programs

  • Mathematica
    r = Sqrt[6]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194746 *)
Table[t[n], {n, 1, 100}]   (* A194747 *)

A194747 Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.

Original entry on oeis.org

0, 0, 2, 1, 4, 2, 6, 3, 8, 4, 0, 7, 2, 10, 4, 13, 6, 16, 8, 0, 12, 3, 16, 6, 20, 9, 24, 12, 28, 15, 2, 20, 6, 25, 10, 30, 14, 35, 18, 1, 24, 6, 30, 11, 36, 16, 42, 21, 48, 26, 4, 33, 10, 40, 16, 47, 22, 54, 28, 2, 36, 9, 44, 16, 52, 23, 60, 30, 68, 37, 6, 46, 14, 55, 22, 64
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194746, A194738.

Programs

  • Mathematica
    r = Sqrt[6]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194746 *)
Table[t[n], {n, 1, 100}]   (* A194747 *)

A194748 Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.

Original entry on oeis.org

1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 8, 3, 11, 5, 14, 7, 17, 9, 1, 13, 4, 17, 7, 21, 10, 25, 13, 29, 16, 3, 21, 7, 26, 11, 31, 15, 36, 19, 2, 25, 7, 31, 12, 37, 17, 43, 22, 49, 27, 5, 34, 11, 41, 17, 48, 23, 55, 29, 3, 37, 10, 45, 17, 53, 24, 61, 31, 69, 38, 7, 47, 15, 56, 23
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194749, A194738.

Programs

  • Mathematica
    r = -Sqrt[6]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194748 *)
Table[t[n], {n, 1, 100}]   (* A194749 *)

A194749 Number of k such that {-k*sqrt(6)} > {-n*sqrt(6)}, where { } = fractional part.

Original entry on oeis.org

0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 10, 4, 10, 3, 10, 2, 10, 1, 10, 19, 8, 18, 6, 17, 4, 16, 2, 15, 0, 14, 28, 11, 26, 8, 24, 5, 22, 2, 20, 38, 16, 35, 12, 32, 8, 29, 4, 26, 0, 23, 46, 18, 42, 13, 38, 8, 34, 3, 30, 57, 24, 52, 18, 47, 12, 42, 6, 37, 0, 32, 64, 25, 58, 18, 52, 11
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194748, A194738.

Programs

  • Mathematica
    r = -Sqrt[6]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194748 *)
Table[t[n], {n, 1, 100}]   (* A194749 *)

A194751 Number of k such that {k*e} > {n*e}, where { } = fractional part.

Original entry on oeis.org

0, 1, 2, 0, 2, 4, 6, 1, 4, 7, 0, 4, 8, 12, 2, 7, 12, 0, 6, 12, 18, 3, 10, 17, 0, 8, 16, 24, 4, 13, 22, 0, 10, 20, 30, 5, 16, 27, 38, 10, 22, 34, 4, 17, 30, 43, 10, 24, 38, 3, 18, 33, 48, 10, 26, 42, 2, 19, 36, 53, 10, 28, 46, 1, 20, 39, 58, 10, 30, 50, 0, 21, 42, 63, 10, 32
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194750, A194738.

Programs

  • Mathematica
    r = E; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194750 *)
Table[t[n], {n, 1, 100}]   (* A194751 *)

A194752 Number of k such that {-k*e} < {-n*e}, where { } = fractional part.

Original entry on oeis.org

1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 1, 5, 9, 13, 3, 8, 13, 1, 7, 13, 19, 4, 11, 18, 1, 9, 17, 25, 5, 14, 23, 1, 11, 21, 31, 6, 17, 28, 39, 11, 23, 35, 5, 18, 31, 44, 11, 25, 39, 4, 19, 34, 49, 11, 27, 43, 3, 20, 37, 54, 11, 29, 47, 2, 21, 40, 59, 11, 31, 51, 1, 22, 43, 64, 11, 33
Offset: 1

Views

Author

Clark Kimberling, Sep 02 2011

Keywords

Crossrefs

Cf. A194753, A194738.

Programs

  • Mathematica
    r = -E; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]
v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]
s[n_] := Sum[u[n, k], {k, 1, n}]
t[n_] := Sum[v[n, k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194752 *)
Table[t[n], {n, 1, 100}]   (* A194753 *)
Previous Showing 11-20 of 33 results. Next

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