A184929 a(n) = n + [rn/s] + [tn/s] + [un/s], where []=floor and r=sin(Pi/2), s=sin(Pi/3), t=sin(Pi/4), u=sin(Pi/5).

2, 6, 10, 13, 17, 20, 24, 28, 32, 35, 38, 42, 46, 50, 54, 57, 60, 64, 67, 72, 76, 78, 82, 86, 89, 94, 98, 101, 104, 108, 112, 115, 119, 123, 126, 130, 134, 137, 141, 145, 148, 152, 156, 158, 162, 167, 170, 174, 178, 180, 184, 189, 192, 196, 199, 203, 206, 210, 215, 217, 221, 225, 228, 232, 237, 239, 243, 247, 250, 254, 257, 261, 265, 269, 272, 276, 279, 283, 287, 291, 294, 297, 301, 305, 309, 313, 317, 319, 323, 327, 331, 335, 338, 341, 345, 349, 353, 357, 360, 363, 367, 371, 374, 378, 382, 385, 389, 393, 395, 400, 404, 408, 411, 415, 418, 421, 426, 430, 433, 436

Offset: 1

Author

Clark Kimberling, Jan 26 2011

Keywords

• nonn

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*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. A184928, A184930, 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 *)