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 1-3 of 3 results.

A184924 n+[sn/r]+[tn/r]+[un/r], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

Original entry on oeis.org

6, 14, 21, 28, 37, 44, 52, 59, 67, 75, 83, 89, 98, 106, 112, 120, 128, 136, 143, 150, 158, 167, 173, 181, 189, 197, 204, 212, 219, 227, 235, 242, 250, 257, 265, 273, 280, 287, 296, 303, 311, 318, 326, 334, 341, 348, 357, 364, 371, 379, 387, 395, 402, 409, 417, 425, 432, 440, 448, 455, 463, 471, 478, 486, 493, 501, 509, 516, 524, 532, 538, 546, 555, 562, 569, 577, 585, 593, 600, 607, 616, 623, 630, 638, 646, 653, 661, 668, 677, 684, 691, 699, 707, 714, 722, 729, 737, 745, 752, 760, 767, 775, 783, 791, 797, 806, 814, 821, 828, 836, 844, 851, 858, 866, 875, 881, 889, 897, 905, 912
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184927 partition the positive integers:
A184924: 6,14,21,28,37,44,52,59,...
A184925: 3,8,11,17,20,25,30,34,...
A184926: 2,5,9,12,15,19,23,26,29,...
A184927: 1,4,7,10,13,16,18,22,24,...
Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
where h>=1, i>=1, j>=1, k>=1. The position of n*r in the joint ranking is n+[sn/r]+[tn/r]+[un/r], and likewise for the positions of n*s, n*t, and n*u.

Crossrefs

Cf. A184912, A184916, A184920, A184925, A184926, A184927.

Programs

  • Mathematica
    r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
Table[a[n],{n,1,120}]  (* A184924 *)
Table[b[n],{n,1,120}]  (* A184925 *)
Table[c[n],{n,1,120}]  (* A184926 *)
Table[d[n],{n,1,120}]  (* A184927 *)

A184925 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

Original entry on oeis.org

3, 8, 11, 17, 20, 25, 30, 34, 38, 42, 47, 51, 55, 61, 64, 69, 72, 78, 82, 86, 92, 95, 100, 103, 109, 113, 117, 122, 126, 130, 135, 139, 144, 147, 153, 156, 161, 166, 170, 175, 178, 184, 187, 192, 196, 201, 205, 209, 214, 218, 222, 228, 231, 236, 241, 245, 249, 253, 259, 262, 267, 271, 276, 279, 284, 289, 293, 297, 302, 306, 310, 314, 320, 324, 328, 333, 337, 342, 345, 351, 354, 359, 363, 368, 372, 377, 381, 385, 389, 394, 399, 403, 408, 412, 416, 420, 426, 429, 434, 438, 443, 446, 451, 456, 460, 464, 469, 473, 477, 483, 487, 491, 495, 500, 504, 508, 513, 518, 521, 526
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184927 partition the positive integers:
A184924: 6,14,21,28,37,44,52,59,...
A184925: 3,8,11,17,20,25,30,34,...
A184926: 2,5,9,12,15,19,23,26,29,...
A184927: 1,4,7,10,13,16,18,22,24,...
Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
where h>=1, i>=1, j>=1, k>=1. The position of n*s in the joint ranking is n+[rn/s]+[tn/s]+[un/s], and likewise for the positions of n*r, n*t, and n*u.

Crossrefs

Cf. A184924, A184926, A184927.

Programs

  • Mathematica
    r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
Table[a[n],{n,1,120}]  (* A184924 *)
Table[b[n],{n,1,120}]  (* A184925 *)
Table[c[n],{n,1,120}]  (* A184926 *)
Table[d[n],{n,1,120}]  (* A184927 *)

A184927 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).

Original entry on oeis.org

1, 4, 7, 10, 13, 16, 18, 22, 24, 27, 31, 33, 35, 39, 41, 45, 48, 50, 54, 56, 58, 62, 65, 68, 71, 73, 76, 79, 81, 85, 88, 91, 93, 96, 99, 102, 105, 108, 110, 114, 116, 119, 123, 125, 129, 131, 133, 137, 140, 142, 146, 148, 151, 154, 157, 160, 163, 165, 168, 171, 174, 177, 180, 183, 185, 188, 191, 194, 198, 200, 203, 206, 208, 211, 215, 217, 221, 223, 225, 229, 232, 234, 238, 239, 243, 246, 248, 252, 255, 258, 260, 263, 266, 269, 272, 275, 277, 281, 283, 286, 290, 292, 295, 298, 300, 304, 307, 309, 313, 315, 317, 321, 323, 327, 330, 332, 335, 338, 340, 344
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184927 partition the positive integers:
A184924: 6,14,21,28,37,44,52,59,...
A184925: 3,8,11,17,20,25,30,34,...
A184926: 2,5,9,12,15,19,23,26,29,...
A184927: 1,4,7,10,13,16,18,22,24,...
Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
where h>=1, i>=1, j>=1, k>=1. The position of n*u in the joint ranking is n+[rn/u]+[sn/u]+[tn/u], and likewise for the positions of n*r, n*s, and n*t.

Crossrefs

Cf. A184924, A184925, A184926.

Programs

  • Mathematica
    r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
Table[a[n],{n,1,120}]  (* A184924 *)
Table[b[n],{n,1,120}]  (* A184925 *)
Table[c[n],{n,1,120}]  (* A184926 *)
Table[d[n],{n,1,120}]  (* A184927 *)
With[{c=Sqrt[7]},Table[n+Floor[n/c]+Floor[(n Sqrt[3])/c]+Floor[(n Sqrt[5])/c],{n,120}]] (* Harvey P. Dale, Aug 28 2025 *)

Extensions

Definition corrected by Georg Fischer, Jun 10 2020
Showing 1-3 of 3 results.

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

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