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.

Previous Showing 11-20 of 24 results. Next

A190762 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),2,1) and [ ]=floor.

Original entry on oeis.org

2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1
Offset: 1

Views

Author

Clark Kimberling, May 19 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190763-A190765.

Programs

  • Mathematica
    r = Sqrt[1/2]; b = 2; c = 1;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190762 *)
Flatten[Position[t, 0]]      (* A190763 *)
Flatten[Position[t, 1]]      (* A190764 *)
Flatten[Position[t, 2]]      (* A190765 *)

A190488 Positions of 0 in A190487.

Original entry on oeis.org

3, 5, 8, 10, 15, 17, 20, 22, 27, 29, 32, 34, 37, 39, 44, 46, 49, 51, 56, 58, 61, 63, 68, 73, 75, 78, 80, 85, 87, 90, 92, 97, 99, 102, 104, 107, 109, 114, 116, 119, 121, 126, 128, 131, 133, 136, 138, 143, 145, 148, 150, 155, 157, 160, 162, 167, 169, 172, 174, 177, 179, 184, 186, 189, 191, 196, 198, 201, 203, 206, 208, 213, 215, 218
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Comments

See A190487.

Links

Crossrefs

Cf. A190487.

Programs

  • Mathematica
    r = Sqrt[2]; b = 3; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}]  (* A190487 *)
Flatten[Position[t, 0]]   (* A190488 *)
Flatten[Position[t, 1]]   (* A190489 *)
Flatten[Position[t, 2]]   (* A190490 *)

A190489 Positions of 1 in A190487.

Original entry on oeis.org

1, 4, 6, 11, 13, 16, 18, 23, 25, 28, 30, 35, 40, 42, 45, 47, 52, 54, 57, 59, 64, 66, 69, 71, 74, 76, 81, 83, 86, 88, 93, 95, 98, 100, 103, 105, 110, 112, 115, 117, 122, 124, 127, 129, 134, 139, 141, 144, 146, 151, 153, 156, 158, 163, 165, 168, 170, 173, 175, 180, 182, 185, 187, 192, 194, 197, 199, 204, 209, 211, 214, 216, 221, 223
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Links

Crossrefs

Cf. A190487.

Programs

  • Mathematica
    r = Sqrt[2]; b = 3; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}]  (* A190487 *)
Flatten[Position[t, 0]]   (* A190488 *)
Flatten[Position[t, 1]]   (* A190489 *)
Flatten[Position[t, 2]]   (* A190490 *)

A190555 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,2) and []=floor.

Original entry on oeis.org

2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0
Offset: 1

Views

Author

Clark Kimberling, May 12 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500

Crossrefs

Cf. A190556-A190559, A190486.

Programs

  • Mathematica
    r = Sqrt[2]; b = 4; c = 2;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190555 *)
Flatten[Position[t, 0]]          (* A190556 *)
Flatten[Position[t, 1]]          (* A190557 *)
Flatten[Position[t, 2]]          (* A190558 *)
Flatten[Position[t, 3]]          (* A190559 *)
Flatten[Position[t, 4]]          (* A190486 *)

A190676 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,0) and [ ]=floor.

Original entry on oeis.org

2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 2, 1
Offset: 1

Views

Author

Clark Kimberling, May 16 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190677, A190678, A190679, A022838.

Programs

  • Mathematica
    r = Sqrt[3]; b = 3; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190676 *)
Flatten[Position[t, 0]]      (* A190677 *)
Flatten[Position[t, 1]]      (* A190678 *)
Flatten[Position[t, 2]]      (* A190679 *)
Table[Floor[3n Sqrt[3]]-3Floor[n Sqrt[3]],{n,140}] (* Harvey P. Dale, Mar 24 2013 *)

Formula

a(n)=[3n*sqrt(3)]-3[n*sqrt(3)].

Extensions

Definition (Name) corrected by Harvey P. Dale, Mar 24 2013

A190683 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,1) and [ ]=floor.

Original entry on oeis.org

2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 2, 1, 3
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190684-A190687.

Programs

  • Mathematica
    r = Sqrt[3]; b = 3; c = 1;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190683 *)
Flatten[Position[t, 0]]      (* A190684 *)
Flatten[Position[t, 1]]      (* A190685 *)
Flatten[Position[t, 2]]      (* A190686 *)
Flatten[Position[t, 3]]      (* A190687 *)

A190688 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,2) and [ ]=floor.

Original entry on oeis.org

2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 1, 3, 2, 1, 0, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 0, 3, 2
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190689-A190692.

Programs

  • Mathematica
    r = Sqrt[3]; b = 3; c = 2;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190688 *)
Flatten[Position[t, 0]]      (* A190689 *)
Flatten[Position[t, 1]]      (* A190690 *)
Flatten[Position[t, 2]]      (* A190691 *)
Flatten[Position[t, 3]]      (* A190692 *)

A190693 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,0) and [ ]=floor.

Original entry on oeis.org

2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 3, 2, 0, 3, 2, 1, 0, 3
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190694-A190697.

Programs

  • Mathematica
    r = Sqrt[3]; b = 4; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190693 *)
Flatten[Position[t, 0]]      (* A190694 *)
Flatten[Position[t, 1]]      (* A190695 *)
Flatten[Position[t, 2]]      (* A190696 *)
Flatten[Position[t, 3]]      (* A190697 *)

Formula

a(n)=[4n*sqrt(3)]-4[n*sqrt(3)].

A190704 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,2) and [ ]=floor.

Original entry on oeis.org

3, 2, 1, 4, 3, 2, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 2, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 2
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190673, A190706-A190709.

Programs

  • Mathematica
    r = Sqrt[3]; b = 4; c = 2;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190704 *)
Flatten[Position[t, 0]]      (* A190673 *)
Flatten[Position[t, 1]]      (* A190706 *)
Flatten[Position[t, 2]]      (* A190707 *)
Flatten[Position[t, 3]]      (* A190708 *)
Flatten[Position[t, 4]]      (* A190709 *)
With[{r=Sqrt[3],nn=140},Table[Floor[(4n+2)r]-4Floor[n r]-Floor[2r],{n,nn}]] (* Harvey P. Dale, Mar 18 2023 *)

A190770 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,1) and [ ]=floor.

Original entry on oeis.org

2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1
Offset: 1

Views

Author

Clark Kimberling, May 19 2011

Keywords

Comments

Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 (or b) position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A190480-A190482
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566

Crossrefs

Cf. A190771-A190774.

Programs

  • Mathematica
    r = Sqrt[1/2]; b = 3; c = 1;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190770 *)
Flatten[Position[t, 0]]      (* A190771 *)
Flatten[Position[t, 1]]      (* A190772 *)
Flatten[Position[t, 2]]      (* A190773 *)
Flatten[Position[t, 3]]      (* A190774 *)
Previous Showing 11-20 of 24 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.