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.

A206912 Position of log(n+1) when the partial sums of the harmonic series are jointly ranked with the set {log(k+1)}; complement of A206911.

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 71, 73, 75, 76, 78, 79, 81, 82, 84, 85, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 103, 104
Offset: 1

Views

Author

Clark Kimberling, Feb 13 2012

Keywords

Comments

Conjecture: the difference sequence of A206912 consists of 1s and 2s; see Comments at A206911.

Examples

			(See the example at A206911.)

Crossrefs

Cf. A206911.

Programs

  • Mathematica
    f[n_] := Sum[1/k, {k, 1, n}];  z = 300;
g[n_] := N[Log[n + 1]];
c = Table[f[n], {n, 1, z}];
s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]]; q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]]    (* A206911 *)
Flatten[Table[q[n], {n, 1, z}]]    (* A206912 *)

A207672 n + [ns/r] + [nt/r], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 9, 10, 12, 14, 15, 16, 18, 19, 20, 22, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 38, 40, 41, 42, 44, 45, 47, 49, 50, 51, 52, 54, 55, 56, 59, 60, 61, 63, 64, 65, 67, 68, 70, 72, 73, 74, 76, 77, 78, 80, 82, 83, 85, 86, 87, 89, 90, 91, 94, 95, 96, 98
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2012

Keywords

Comments

The sequences A207672, A207673, A208326 partition the positive integers. To generate them, jointly rank the sets {i/r}, {j/s}, {k*s}. The positions of n/r in the joint ranking form A207672, and likewise for the other sequences.
For a guide to related sequences and a conjecture, see A206911.

Crossrefs

Cf. A206911, A207673, A208326.

Programs

  • Mathematica
    r = 5; s = GoldenRatio; t = 1/s;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 60}]  (* A207672 *)
Table[b[n], {n, 1, 60}]  (* A207673 *)
Table[c[n], {n, 1, 60}]  (* A208326 *)

A207673 n+[nr/s]+[nt/s], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

Original entry on oeis.org

4, 8, 13, 17, 21, 26, 30, 35, 39, 43, 48, 53, 57, 62, 66, 71, 75, 79, 84, 88, 93, 97, 102, 107, 111, 115, 120, 124, 129, 133, 137, 142, 146, 151, 156, 160, 165, 169, 173, 178, 182, 187, 191, 195, 201, 205, 209, 214, 218, 223, 227, 231, 236, 240, 245
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2012

Keywords

Comments

The sequences A207672, A207673, A208326 partition the positive integers. To generate them, jointly rank the sets {i/r}, {j/s}, {k*s}. The positions of n/r in the joint ranking form A207672, and likewise for the other sequences.
For a guide to related sequences and conjectures, see A206911.

Crossrefs

Cf. A206911, A207672, A208326.

Programs

  • Mathematica
    r = 5; s = GoldenRatio; t = 1/s;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 60}]  (* A207672 *)
Table[b[n], {n, 1, 60}]  (* A207673 *)
Table[c[n], {n, 1, 60}]  (* A208326 *)

Extensions

Definition corrected by Georg Fischer, Jun 10 2020

A208326 n + [nr/t] + [ns/t], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.

Original entry on oeis.org

11, 23, 34, 46, 58, 69, 81, 92, 104, 116, 127, 140, 152, 163, 175, 186, 198, 210, 221, 233, 244, 256, 269, 280, 292, 304, 315, 327, 338, 350, 362, 373, 385, 398, 409, 421, 432, 444, 456, 467, 479, 490, 502, 514, 526, 538, 550, 561, 573, 584, 596
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2012

Keywords

Comments

The sequences A207672, A207673, A208326 partition the positive integers. To generate them, jointly rank the sets {i/r}, {j/s}, {k*s}. The positions of n/r in the joint ranking form A207672, and likewise for the other sequences.
For a guide to related sequences and conjectures, see A206911.

Crossrefs

Cf. A206911, A207672, A207673.

Programs

  • Mathematica
    r = 5; s = GoldenRatio; t = 1/s;
a[n_] := n + Floor[n*s/r] + Floor[n*t/r];
b[n_] := n + Floor[n*r/s] + Floor[n*t/s];
c[n_] := n + Floor[n*r/t] + Floor[n*s/t];
Table[a[n], {n, 1, 60}]  (* A207672 *)
Table[b[n], {n, 1, 60}]  (* A207673 *)
Table[c[n], {n, 1, 60}]  (* A208326 *)

A185392 Position of g(n) when the numbers f(j) and g(k) are jointly ranked, where f(j) = j + |cos j| and g(k) = k + |sin k|.

Original entry on oeis.org

2, 4, 5, 8, 10, 11, 13, 16, 17, 19, 22, 23, 25, 28, 29, 31, 34, 36, 37, 40, 42, 43, 46, 48, 49, 52, 54, 55, 57, 60, 61, 63, 66, 67, 69, 72, 73, 75, 78, 80, 81, 84, 86, 87, 90, 92, 93, 96, 98, 99, 101, 104, 105, 107, 110, 111, 113, 116, 117, 119, 122, 124, 125
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2012

Keywords

Comments

For a guide to related sequences and a conjecture, see A206911.

Links

Crossrefs

Cf. A206911, A208327.

Programs

  • Mathematica
    f[n_] := N[n + Abs[Cos[n]]]; g[n_] := N[n + Abs[Sin[n]]]; z = 90;
c = Table[f[n], {n, 1, z}];
s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]];
q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]]  (* A208327 *)
Flatten[Table[q[n], {n, 1, z}]]  (* A185392 *)

A208327 Position of f(n) when the numbers f(j) and g(k) are jointly ranked, where f(j)=j + |cos j | and g(k)=k + |sin k|.

Original entry on oeis.org

1, 3, 6, 7, 9, 12, 14, 15, 18, 20, 21, 24, 26, 27, 30, 32, 33, 35, 38, 39, 41, 44, 45, 47, 50, 51, 53, 56, 58, 59, 62, 64, 65, 68, 70, 71, 74, 76, 77, 79, 82, 83, 85, 88, 89, 91, 94, 95, 97, 100, 102, 103, 106, 108, 109, 112, 114, 115, 118, 120, 121, 123, 126
Offset: 1

Views

Author

Clark Kimberling, Feb 26 2012

Keywords

Comments

For a guide to related sequences and a conjecture, see A206911.

Links

Crossrefs

Cf. A185392, A206911.

Programs

  • Mathematica
    f[n_] := N[n + Abs[Cos[n]]]; g[n_] := N[n + Abs[Sin[n]]]; z = 90;
c = Table[f[n], {n, 1, z}];
s = Table[g[n], {n, 1, z}];
j = Sort[Union[c, s]];
p[n_] := Position[j, f[n]];
q[n_] := Position[j, g[n]];
Flatten[Table[p[n], {n, 1, z}]]  (* A208327 *)
Flatten[Table[q[n], {n, 1, z}]]  (* A185392 *)
Showing 1-6 of 6 results.

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