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A184912 n+[ns/r]+[nt/r]+[nu/r], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

%I A184912 #6 Mar 30 2012 18:57:17
%S A184912 4,9,13,19,23,28,34,39,43,49,53,58,63,69,73,79,83,88,93,98,103,109,
%T A184912 113,118,122,128,133,138,143,148,152,158,163,168,174,178,183,188,193,
%U A184912 197,204,208,213,218,223,227,233,238,243,247,253,257,262,268,273,277,283,287,292,297,303,307,313,318,322,328,332,338,343,348,352,358,362,368,372,378,382,387,392,397,402,408,412,417,422,427,431,438,442,447,452,457,461,467,472,477,482,487,492,496,503,507,512,517,522,526,532,537,542,547,552,556,562,566,572,577,582,586,592,596
%N A184912 n+[ns/r]+[nt/r]+[nu/r], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.
%C A184912 The sequences A184912-A184915 partition the positive integers:
%C A184912   A184912: 4,9,13,19,23,28,34,...
%C A184912   A184913: 3,7,11,16,20,24,30,...
%C A184912   A184914: 2,6,10,14,17,21,26,...
%C A184912   A184915: 1,5,8,12,15,18,22,...
%C A184912 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.
%C A184912 The position of n*r in the joint ranking is
%C A184912   n+[sn/r]+[tn/r]+[un/r], and likewise for the
%C A184912   positions of n*s, n*t, and n*u.
%F A184912 a(n)=n+[ns/r]+[nt/r]+[nu/r], where []=floor and
%F A184912 r=2^(1/5), s=r^2, t=r^3, u=r^4.
%t A184912 r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);
%t A184912 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184912 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184912 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184912 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184912 Table[a[n],{n,1,120}]  (* A184912 *)
%t A184912 Table[b[n],{n,1,120}]  (* A184913 *)
%t A184912 Table[c[n],{n,1,120}]  (* A184914 *)
%t A184912 Table[d[n],{n,1,120}]  (* A184915 *)
%Y A184912 Cf. A184312, A184913, A184914, A184915.
%K A184912 nonn
%O A184912 1,1
%A A184912 _Clark Kimberling_, Jan 25 2011