OFFSET
1,1
COMMENTS
A184916: 4,9,15,19,25,31,35,41,...
A184917: 3,7,12,16,21,26,29,34,...
A184918: 2,6,10,13,17,22,24,28,...
A184919: 1,5,8,11,14,18,20,23,27,...
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*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.
FORMULA
a(n)=n+[sn/r]+[tn/r]+[un/r], where []=floor and
r=1, s=2^(1/4), t=s^2, u=s^3.
MATHEMATICA
r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
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}] (* A184916 *)
Table[b[n], {n, 1, 120}] (* A184917 *)
Table[c[n], {n, 1, 120}] (* A184918 *)
Table[d[n], {n, 1, 120}] (* A184919 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 26 2011
STATUS
approved