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 1-10 of 24 results. Next

A190495 Positions of 3 in A190491.

Original entry on oeis.org

7, 12, 19, 24, 36, 41, 48, 53, 65, 70, 77, 82, 89, 94, 106, 111, 118, 123, 135, 140, 147, 152, 164, 176, 181, 188, 193, 205, 210, 217, 222, 234, 239, 246, 251, 258, 263, 275, 280, 287, 292, 304, 309, 316, 321, 328, 333, 345, 350, 357, 362, 374, 379, 386, 391, 403, 408, 415, 420
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Comments

See A190492.

Links

Crossrefs

Cf. A190491.

Programs

A190492 Positions of 0 in A190491.

Original entry on oeis.org

5, 10, 17, 22, 27, 29, 34, 39, 46, 51, 58, 63, 68, 75, 80, 87, 92, 97, 99, 104, 109, 116, 121, 126, 128, 133, 138, 145, 150, 157, 162, 167, 169, 174, 179, 186, 191, 196, 198, 203, 208, 215, 220, 227, 232, 237, 244, 249, 256, 261, 266, 268, 273, 278, 285, 290, 295, 297, 302, 307, 314, 319, 326, 331, 336, 338, 343, 348, 355, 360, 365
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Comments

See A190491.

Links

Crossrefs

Cf. A190491.

Programs

A190493 Positions of 1 in A190491.

Original entry on oeis.org

1, 3, 6, 8, 13, 15, 18, 20, 23, 25, 30, 32, 35, 37, 42, 44, 47, 49, 54, 56, 59, 61, 64, 66, 71, 73, 76, 78, 83, 85, 88, 90, 93, 95, 100, 102, 105, 107, 112, 114, 117, 119, 124, 129, 131, 134, 136, 141, 143, 146, 148, 153, 155, 158, 160, 163, 165, 170, 172, 175, 177, 182, 184, 187, 189, 194, 199, 201, 204, 206, 211, 213, 216, 218, 223
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Comments

(See A190492.)

Links

Crossrefs

Cf. A190491.

Programs

A190494 Positions of 2 in A190491.

Original entry on oeis.org

2, 4, 9, 11, 14, 16, 21, 26, 28, 31, 33, 38, 40, 43, 45, 50, 52, 55, 57, 60, 62, 67, 69, 72, 74, 79, 81, 84, 86, 91, 96, 98, 101, 103, 108, 110, 113, 115, 120, 122, 125, 127, 130, 132, 137, 139, 142, 144, 149, 151, 154, 156, 159, 161, 166, 168, 171, 173, 178, 180, 183, 185, 190, 192, 195, 197, 200, 202, 207, 209, 212, 214, 219
Offset: 1

Views

Author

Clark Kimberling, May 11 2011

Keywords

Comments

See A190491.

Links

Crossrefs

Cf. A190491.

Programs

A190487 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,0) and []=floor.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 11 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
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500

Links

Crossrefs

Cf. A190488, A190489, A190490.

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 *)

A190496 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,2) and []=floor.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 11 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
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500

Links

Crossrefs

Cf. A190497, A190498, A190499, A190500.

Programs

  • Mathematica
    r = Sqrt[2]; 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}]  (* A190496 *)
Flatten[Position[t, 0]]   (* A190497 *)
Flatten[Position[t, 1]]   (* A190498 *)
Flatten[Position[t, 2]]   (* A190499 *)
Flatten[Position[t, 3]]   (* A190500 *)

A190483 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),2,1) and []=floor.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 11 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
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500

Links

Crossrefs

Cf. A190484, A190485, A190486.

Programs

  • Mathematica
    r = Sqrt[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}]  (* A190483 *)
Flatten[Position[t, 0]]   (* A190484 *)
Flatten[Position[t, 1]]   (* A190485 *)
Flatten[Position[t, 2]]   (* A190486 *)
  • Python
    from sympy import sqrt, floor
r=sqrt(2)
def a(n): return floor((2*n + 1)*r) - 2*floor(n*r) - floor(r)
print([a(n) for n in range(1, 501)]) # Indranil Ghosh, Jul 02 2017

A190544 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,0) and []=floor.

Original entry on oeis.org

1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 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),2,0): A190480
(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

Links

Crossrefs

Cf. A190545, A190546, A190547, A190548.

Programs

  • Mathematica
    r = Sqrt[2]; 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}] (* A190544 *)
Flatten[Position[t, 0]]      (* A190545 *)
Flatten[Position[t, 1]]      (* A190546 *)
Flatten[Position[t, 2]]      (* A190547 *)
Flatten[Position[t, 3]]      (* A190548 *)

Formula

a(n) = [4nr] - 4*[nr], where r=sqrt(2).

A190549 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,1) and []=floor.

Original entry on oeis.org

2, 3, 1, 3, 0, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3
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),2,0): 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

Links

Crossrefs

Cf. A190550, A190551, A190552, A190553.

Programs

  • Mathematica
    r = Sqrt[2]; b = 4; c = 1;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190549 *)
Flatten[Position[t, 0]]          (* A190550 *)
Flatten[Position[t, 1]]          (* A190551 *)
Flatten[Position[t, 2]]          (* A190552 *)
Flatten[Position[t, 3]]          (* A190553 *)
Flatten[Position[t, 4]]          (* A190554 *)

A190561 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,3) and []=floor.

Original entry on oeis.org

1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 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),2,0): 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

Links

Crossrefs

Cf. A190562 to A190566.

Programs

  • Mathematica
    r = Sqrt[2]; b = 4; c = 3;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190561 *)
Flatten[Position[t, 0]]          (* A190562 *)
Flatten[Position[t, 1]]          (* A190563 *)
Flatten[Position[t, 2]]          (* A190564 *)
Flatten[Position[t, 3]]          (* A190565 *)
Flatten[Position[t, 4]]          (* A190566 *)
Showing 1-10 of 24 results. Next

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