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A184914 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

%I A184914 #4 Mar 30 2012 18:57:17
%S A184914 2,6,10,14,17,21,26,29,32,36,40,44,47,52,56,59,62,66,70,74,78,82,86,
%T A184914 89,92,96,101,105,108,112,115,119,123,127,131,135,139,142,145,149,154,
%U A184914 157,161,165,169,172,175,180,184,187,191,195,199,203,206,210,214,217,221,225,230,232,236,240,244,248,251,256,260,263,266,270,274,279,282,286,290,293,296,300,305,309,312,316,319,323,326,331,335,339,342,346,349,353,357,361,365,369,373,376,380,384,388,391,395,399,403,407,410,414,418,421,425,429,434,436,440,444,448,451
%N A184914 n+[rn/t]+[sn/t]+[un/t], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.
%C A184914 The sequences A184912-A184915 partition the positive integers:
%C A184914   A184912: 4,9,13,19,23,28,34,...
%C A184914   A184913: 3,7,11,16,20,24,30,...
%C A184914   A184914: 2,6,10,14,17,21,26,...
%C A184914   A184915: 1,5,8,12,15,18,22,...
%C A184914 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 A184914 The position of n*t in the joint ranking is
%C A184914 n+[rn/t]+[sn/t]+[un/t], and likewise for the
%C A184914 positions of n*r, n*s, and n*u.
%t A184914 r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);
%t A184914 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184914 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184914 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184914 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184914 Table[a[n],{n,1,120}]  (* A184912 *)
%t A184914 Table[b[n],{n,1,120}]  (* A184913 *)
%t A184914 Table[c[n],{n,1,120}]  (* A184914 *)
%t A184914 Table[d[n],{n,1,120}]  (* A184915 *)
%Y A184914 Cf. A184812, A184912, A184913, A184915.
%K A184914 nonn
%O A184914 1,1
%A A184914 _Clark Kimberling_, Jan 25 2011