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.

A184928 a(n) = n + [sn/r] + [tn/r] + [un/r], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

Original entry on oeis.org

1, 5, 8, 11, 14, 18, 21, 23, 27, 30, 33, 37, 40, 43, 45, 49, 52, 55, 59, 62, 65, 68, 71, 74, 77, 81, 84, 87, 91, 93, 96, 99, 103, 106, 109, 113, 116, 118, 121, 125, 128, 131, 135, 138, 140, 144, 147, 150, 153, 157, 160, 163, 166, 169, 172, 175, 179, 183, 185, 188, 191, 194, 198, 201, 204, 207, 211, 213, 216, 220, 223, 226, 229, 233, 236, 238, 242, 245, 248, 252, 255, 258, 260, 264, 267, 270, 274, 277, 280, 282, 286, 290, 292, 296, 299, 302, 306, 308, 312, 314, 318, 321, 324, 328, 330, 333, 336, 340, 344, 346, 350, 352, 355, 359, 362, 366, 368, 372, 375, 377
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184928 partition the positive integers:
A184928: 1, 5, 6, 11, 14, 18, 21, 23, 27, ...
A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
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. A184929, A184930, A184931; also, A184912, A184916, A184920, A184924.

Programs

  • Mathematica
    r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
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}]  (* A184928 *)
Table[b[n],{n,1,120}]  (* A184929 *)
Table[c[n],{n,1,120}]  (* A184930 *)
Table[d[n],{n,1,120}]  (* A184931 *)

A184930 a(n) = n + [rn/t] + [sn/t] + [un/t], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

Original entry on oeis.org

3, 7, 12, 16, 22, 25, 29, 34, 39, 44, 48, 51, 56, 61, 66, 70, 75, 79, 83, 88, 92, 97, 102, 105, 110, 114, 120, 124, 129, 132, 136, 142, 146, 151, 155, 159, 164, 168, 173, 177, 182, 186, 190, 195, 200, 205, 209, 212, 218, 222, 227, 231, 235, 240, 244, 249, 253, 259, 263, 266, 271, 275, 281, 285, 289, 293, 298, 303, 307, 311, 316, 320, 325, 329, 334, 339, 343, 347, 351, 356, 361, 365, 369, 373, 379, 383, 388, 392, 396, 401, 405, 410, 414, 419, 423, 427, 432, 437, 442, 446, 449, 454, 459, 464, 468, 472, 477, 481, 486, 490, 494, 500, 503, 508, 512, 518, 522, 526, 530, 534
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184928 partition the positive integers:
A184928: 1, 5, 6, 11, 14, 18, 21, 23, 27, ...
A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
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*t in the joint ranking is n + [rn/t] + [sn/t] + [un/t], and likewise for the positions of n*s, n*t, and n*u.

Crossrefs

Cf. A184928, A184929, A184931.

Programs

  • Mathematica
    r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
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}]  (* A184928 *)
Table[b[n],{n,1,120}]  (* A184929 *)
Table[c[n],{n,1,120}]  (* A184930 *)
Table[d[n],{n,1,120}]  (* A184931 *)

A184931 a(n) = n + [rn/u] + [sn/u] + [tn/u], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

Original entry on oeis.org

4, 9, 15, 19, 26, 31, 36, 41, 47, 53, 58, 63, 69, 73, 80, 85, 90, 95, 100, 107, 111, 117, 122, 127, 133, 139, 143, 149, 154, 161, 165, 171, 176, 181, 187, 193, 197, 202, 208, 214, 219, 224, 230, 234, 241, 246, 251, 256, 262, 268, 273, 278, 284, 288, 295, 300, 304, 310, 315, 322, 326, 332, 337, 342, 348, 354, 358, 364, 370, 376, 380, 386, 391, 397, 402, 407, 413, 417, 424, 429, 434, 439, 445, 450, 456, 461, 467, 471, 478, 483, 488, 493, 499, 504, 509, 515, 520, 525, 531, 537, 541, 547, 552, 558, 563, 569, 574, 579, 585, 591, 595, 601, 606, 611, 617, 622, 628, 632, 639, 644
Offset: 1

Views

Author

Clark Kimberling, Jan 26 2011

Keywords

Comments

The sequences A184924-A184928 partition the positive integers:
A184928: 1, 5, 6, 11, 14, 18, 21, 23, 27, ...
A184929: 2, 6, 10, 13, 17, 20, 24, 28, 32, ...
A184930: 3, 7, 12, 16, 22, 25, 29, 34, 39, ...
A184931: 4, 9, 15, 19, 26, 31, 36, 41, 47, ...
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. A184928, A184929, A184930.

Programs

  • Mathematica
    r=Sin[Pi/2]; s=Sin[Pi/3]; t=Sin[Pi/4]; u=Sin[Pi/5];
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}]  (* A184928 *)
Table[b[n],{n,1,120}]  (* A184929 *)
Table[c[n],{n,1,120}]  (* A184930 *)
Table[d[n],{n,1,120}]  (* A184931 *)
Showing 1-3 of 3 results.

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