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.

A184916 n+[sn/r]+[tn/r]+[un/r], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

Original entry on oeis.org

4, 9, 15, 19, 25, 31, 35, 41, 46, 51, 57, 62, 67, 72, 78, 83, 89, 94, 98, 104, 109, 115, 120, 125, 131, 135, 142, 147, 152, 157, 162, 168, 173, 179, 183, 188, 195, 199, 205, 210, 214, 220, 226, 231, 236, 242, 247, 252, 258, 263, 268, 273, 279, 284, 289, 295, 299, 305, 311, 315, 321, 326, 331, 337, 342, 347, 352, 358, 364, 368, 374, 379, 384, 390, 396, 400, 405, 411, 415, 422, 427, 431, 437, 442, 448, 453, 459, 463, 468, 475, 480, 485, 490, 495, 500, 506, 512, 516, 522, 527, 532, 538, 543, 548, 553, 559, 564, 569, 575, 579, 585, 591, 596, 601, 606, 612, 617, 622, 628, 632
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184916-A184919 partition the positive integers:
A184916: 4,9,15,19,25,31,35,41,...
A184917: 3,7,12,16,21,26,29,34,...
A184918: 2,6,10,13,17,22,24,28,...
A184919: 1,5,8,11,14,18,20,23,27,...
The joint ranking method of A184812 is extended here to four numbers r,s,t,u, as follows: jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, 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, A184917, A184918, A184919.

Programs

  • Mathematica
    r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
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}]  (* A184916 *)
Table[b[n],{n,1,120}]  (* A184917 *)
Table[c[n],{n,1,120}]  (* A184918 *)
Table[d[n],{n,1,120}]  (* A184919 *)

Formula

a(n)=n+[sn/r]+[tn/r]+[un/r], where []=floor and
r=1, s=2^(1/4), t=s^2, u=s^3.

A184917 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

Original entry on oeis.org

3, 7, 12, 16, 21, 26, 29, 34, 38, 43, 48, 52, 56, 60, 65, 70, 75, 79, 82, 87, 91, 97, 101, 105, 110, 113, 119, 123, 128, 132, 136, 141, 145, 150, 154, 158, 164, 167, 172, 176, 180, 185, 190, 194, 198, 203, 207, 212, 217, 221, 225, 229, 234, 239, 243, 248, 251, 256, 261, 265, 270, 274, 278, 283, 287, 292, 296, 301, 306, 309, 314, 318, 323, 328, 333, 336, 340, 345, 349, 355, 359, 362, 367, 371, 377, 381, 386, 389, 393, 399, 403, 408, 412, 416, 420, 425, 430, 434, 439, 443, 447, 452, 456, 461, 465, 470, 474, 478, 483, 487, 492, 497, 501, 505, 509, 514, 519, 523, 528, 531
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184916-A184919 partition the positive integers:
A184916: 4,9,15,19,25,31,35,41,...
A184917: 3,7,12,16,21,26,29,34,...
A184918: 2,6,10,13,17,22,24,28,...
A184919: 1,5,8,11,14,18,20,23,27,...
The joint ranking method of A184812 is extended here to four numbers r,s,t,u, as follows: jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, 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. A184912, A184916, A184918, A184919.

Programs

  • Mathematica
    r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
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}]  (* A184916 *)
Table[b[n],{n,1,120}]  (* A184917 *)
Table[c[n],{n,1,120}]  (* A184918 *)
Table[d[n],{n,1,120}]  (* A184919 *)

A184919 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

Original entry on oeis.org

1, 5, 8, 11, 14, 18, 20, 23, 27, 30, 33, 37, 39, 42, 45, 49, 53, 55, 58, 61, 64, 68, 71, 74, 77, 80, 84, 86, 90, 93, 96, 99, 102, 106, 108, 112, 116, 117, 121, 124, 127, 130, 134, 137, 139, 143, 146, 149, 153, 156, 159, 161, 165, 169, 171, 175, 177, 181, 184, 187, 191, 193, 196, 200, 202, 206, 209, 213, 216, 218, 222, 224, 228, 232, 235, 237, 240, 244, 246, 250, 254, 255, 259, 262, 266, 269, 272, 275, 277, 281, 285, 288, 291, 294, 297, 300, 303, 307, 310, 313, 316, 319, 322, 325, 329, 332, 334, 338, 341, 344, 348, 351, 354, 356, 360, 363, 366, 370, 373, 375
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184916-A184919 partition the positive integers:
A184916: 4,9,15,19,25,31,35,41,...
A184917: 3,7,12,16,21,26,29,34,...
A184918: 2,6,10,13,17,22,24,28,...
A184919: 1,5,8,11,14,18,20,23,27,...
The joint ranking method of A184812 is extended here to four numbers r,s,t,u, as follows: jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u}, 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. A184912, A184916, A184917, A184918.

Programs

  • Mathematica
     r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
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}]  (* A184916 *)
Table[b[n],{n,1,120}]  (* A184917 *)
Table[c[n],{n,1,120}]  (* A184918 *)
Table[d[n],{n,1,120}]  (* A184919 *)
Table[With[{s=Surd[2,4]},n+Floor[n/s^3]+Floor[(n*s)/s^3]+Floor[(n*s^2)/s^3]],{n,120}] (* Harvey P. Dale, Dec 01 2024 *)
Showing 1-3 of 3 results.

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