OFFSET
1,1
COMMENTS
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*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+[ns/r]+[nt/r]+[nu/r], where []=floor and
r=2^(1/5), s=r^2, t=r^3, u=r^4.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 25 2011
STATUS
approved