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 1-5 of 5 results.

A190698 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,1) and [ ]=floor.

Original entry on oeis.org

3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 2, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 4, 2, 1, 0, 3, 2, 1, 4, 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, 4, 3, 2, 1, 4, 3, 2, 1, 4, 3, 1, 0, 3, 2, 1, 4
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

Links

Crossrefs

Cf. A190699-A190703.

Programs

  • Mathematica
    r = Sqrt[3]; 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}] (* A190698 *)
Flatten[Position[t, 0]]      (* A190699 *)
Flatten[Position[t, 1]]      (* A190700 *)
Flatten[Position[t, 2]]      (* A190701 *)
Flatten[Position[t, 3]]      (* A190702 *)
Flatten[Position[t, 4]]      (* A190703 *)

A190699 Positions of 0 in A190698.

Original entry on oeis.org

11, 26, 41, 52, 67, 82, 97, 108, 123, 138, 153, 164, 179, 194, 220, 235, 250, 261, 276, 291, 306, 317, 332, 347, 362, 373, 388, 403, 429, 444, 459, 470, 485, 500, 515, 526, 541, 556, 571, 582, 597, 612, 638, 653, 668, 679, 694, 709, 724, 735, 750, 765, 791, 806, 821, 832, 847, 862, 877, 888, 903, 918, 933, 944, 959, 974, 1000
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

See A190698.

Links

Crossrefs

Cf. A190698.

Programs

  • Mathematica
    r = Sqrt[3]; 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}] (* A190698 *)
Flatten[Position[t, 0]]      (* A190699 *)
Flatten[Position[t, 1]]      (* A190700 *)
Flatten[Position[t, 2]]      (* A190701 *)
Flatten[Position[t, 3]]      (* A190702 *)
Flatten[Position[t, 4]]      (* A190703 *)

A190700 Positions of 1 in A190698.

Original entry on oeis.org

3, 7, 14, 18, 22, 25, 29, 33, 37, 40, 44, 48, 55, 59, 63, 66, 70, 74, 78, 81, 85, 89, 93, 96, 100, 104, 111, 115, 119, 122, 126, 130, 134, 137, 141, 145, 149, 152, 156, 160, 167, 171, 175, 178, 182, 186, 190, 193, 197, 201, 205, 208, 212, 216, 223, 227, 231, 234, 238, 242, 246, 249, 253, 257, 264, 268, 272, 275, 279, 283, 287, 290
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

See A190698.

Links

Crossrefs

Cf. A190698.

Programs

  • Mathematica
    r = Sqrt[3]; 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}] (* A190698 *)
Flatten[Position[t, 0]]      (* A190699 *)
Flatten[Position[t, 1]]      (* A190700 *)
Flatten[Position[t, 2]]      (* A190701 *)
Flatten[Position[t, 3]]      (* A190702 *)
Flatten[Position[t, 4]]      (* A190703 *)
With[{r=Sqrt[3]},Flatten[Position[Table[Floor[r(4n+1)]-4*Floor[r*n]- Floor[r],{n,300}],1]]] (* Harvey P. Dale, May 25 2013 *)

A190702 Positions of 3 in A190698.

Original entry on oeis.org

1, 5, 9, 12, 16, 20, 24, 27, 31, 35, 42, 46, 50, 53, 57, 61, 65, 68, 72, 76, 83, 87, 91, 94, 98, 102, 106, 109, 113, 117, 121, 124, 128, 132, 139, 143, 147, 150, 154, 158, 162, 165, 169, 173, 177, 180, 184, 188, 195, 199, 203, 206, 210, 214, 218, 221, 225, 229, 233, 236, 240, 244, 247, 251, 255, 259, 262, 266, 270, 274, 277, 281
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

See A190698.

Links

Crossrefs

Cf. A190698.

Programs

  • Mathematica
    r = Sqrt[3]; 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}] (* A190698 *)
Flatten[Position[t, 0]]      (* A190699 *)
Flatten[Position[t, 1]]      (* A190700 *)
Flatten[Position[t, 2]]      (* A190701 *)
Flatten[Position[t, 3]]      (* A190702 *)
Flatten[Position[t, 4]]      (* A190703 *)

A190703 Positions of 4 in A190698.

Original entry on oeis.org

4, 8, 15, 19, 23, 30, 34, 38, 45, 49, 56, 60, 64, 71, 75, 79, 86, 90, 101, 105, 112, 116, 120, 127, 131, 135, 142, 146, 157, 161, 168, 172, 176, 183, 187, 191, 198, 202, 209, 213, 217, 224, 228, 232, 239, 243, 254, 258, 265, 269, 273, 280, 284, 288, 295, 299, 310, 314, 321, 325, 329, 336, 340, 344, 351, 355, 366, 370, 377, 381, 385
Offset: 1

Views

Author

Clark Kimberling, May 17 2011

Keywords

Comments

See A190698.

Links

Crossrefs

Cf. A190698.

Programs

  • Mathematica
    r = Sqrt[3]; 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}] (* A190698 *)
Flatten[Position[t, 0]]      (* A190699 *)
Flatten[Position[t, 1]]      (* A190700 *)
Flatten[Position[t, 2]]      (* A190701 *)
Flatten[Position[t, 3]]      (* A190702 *)
Flatten[Position[t, 4]]      (* A190703 *)
Showing 1-5 of 5 results.

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