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.

Showing 1-6 of 6 results.

A194814 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio).

Original entry on oeis.org

1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 17, 17, 18, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 23, 24, 25, 26, 26, 26, 27, 28, 28, 28, 28, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 33, 34, 35, 36, 36, 36
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Comments

A194813+A194814=A000027 for n>0.

Examples

			{4r+1r}=0.09...; {4r-1r}=0.85...;
{4r+2r}=0.70...; {4r-2r}=0.23...;
{4r+3r}=0.32...; {4r-3r}=0.61...;
{4r+4r}=0.94...; {4r-4r}=0.00...;
so that a(4)=2.

Crossrefs

Cf. A194813, A194738.

Programs

  • Mathematica
    r = GoldenRatio; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194813 *)
Table[t[n], {n, 1, 100}]   (* A194814 *)

A194815 Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(2).

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6, 7, 8, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 19, 19, 19, 20, 21, 22, 23, 23, 23, 23, 24, 25, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 34, 34, 34, 35, 36, 37
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Crossrefs

Cf. A002193, A194816, A194813.
Partial sums of A327177.

Programs

  • Mathematica
    r = Sqrt[2]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194815 *)
Table[t[n], {n, 1, 100}]   (* A194816 *)

A194816 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).

Original entry on oeis.org

1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 10, 11, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 17, 18, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 33, 34, 35, 35, 35, 35, 35
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Crossrefs

Cf. A194815, A194813.

Programs

  • Mathematica
    r = Sqrt[2]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194815 *)
Table[t[n], {n, 1, 100}]   (* A194816 *)

A194817 Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(3).

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 24, 25, 26, 26, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 33, 33, 34, 34, 34, 34, 35, 35, 36, 37
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Crossrefs

Cf. A002194, A194818, A194813.
Partial sums of A327180.

Programs

  • Mathematica
    r = Sqrt[3]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194817 *)
Table[t[n], {n, 1, 100}]   (* A194818 *)

A194818 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(3).

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 18, 19, 19, 20, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 26, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 31, 31, 32, 33, 34, 34, 35, 35, 35, 35
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Crossrefs

Cf. A194817, A194813.

Programs

  • Mathematica
    r = Sqrt[3]; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194817 *)
Table[t[n], {n, 1, 100}]   (* A194818 *)

A194820 Number of integers k in [1,n] such that {n*e+k*e} > {n*e-k*e}, where { } = fractional part.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 16, 16, 16, 16, 17, 18, 18, 19, 20, 21, 21, 22, 22, 22, 23, 24, 25, 25, 26, 26, 26, 27, 28, 29, 29, 30, 30, 30, 30, 31, 32, 32, 33, 33, 33, 33, 34, 35, 35, 36, 36, 36
Offset: 1

Views

Author

Clark Kimberling, Sep 03 2011

Keywords

Crossrefs

Cf. A194819, A194813.

Programs

  • Mathematica
    r = E; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194819 *)
Table[t[n], {n, 1, 100}]   (* A194820 *)
Showing 1-6 of 6 results.

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