_Clark Kimberling (ck6(AT)evansville.edu), _, Jan 25 2011

proposed

approved

allocated for Clark Kimberling

n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

1, 5, 8, 12, 15, 18, 22, 25, 27, 31, 35, 38, 41, 45, 48, 51, 54, 57, 61, 65, 67, 71, 75, 77, 80, 84, 87, 91, 94, 97, 100, 104, 107, 110, 114, 117, 121, 124, 126, 130, 134, 136, 140, 144, 147, 150, 153, 156, 160, 162, 166, 170, 173, 176, 179, 182, 186, 189, 192, 196, 200, 201, 205, 209, 212, 216, 219, 222, 226, 229, 231, 235, 239, 242, 245, 249, 252, 255, 258, 261, 265, 269, 271, 275, 278, 281, 284, 288, 291, 295, 298, 301, 304, 308, 310, 314, 317, 321, 325, 327, 330, 334, 337, 340, 344, 347, 351, 354, 356, 360, 364, 366, 370, 374, 377, 379, 383, 386, 390, 393

1,2

The sequences A184912-A184915 partition the positive integers:

A184912: 4,9,13,19,23,28,34,...

A184913: 3,7,11,16,20,24,30,...

A184914: 2,6,10,14,17,21,26,...

A184915: 1,5,8,12,15,18,22,...

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.

r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);

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}] (* A184912 *)

Table[b[n], {n, 1, 120}] (* A184913 *)

Table[c[n], {n, 1, 120}] (* A184914 *)

Table[d[n], {n, 1, 120}] (* A184915 *)

Cf. A184812, A184912, A184913, A184914.

allocated

nonn

Clark Kimberling (ck6(AT)evansville.edu), Jan 25 2011

approved

proposed

allocated for Clark Kimberling

allocated

approved