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).

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

1,2

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.

Links

Table of n, a(n) for n=1..120.

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 *)

Crossrefs

Cf. A184929, A184930, A184931; also, A184912, A184916, A184920, A184924.

Sequence in context: A104279 A184919 A063247 * A186238 A352623 A314389

Adjacent sequences: A184925 A184926 A184927 * A184929 A184930 A184931

Keyword

nonn

Author

Clark Kimberling, Jan 26 2011

Status

approved