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).

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

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*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 *)