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A184917 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.

%I A184917 #4 Mar 30 2012 18:57:17
%S A184917 3,7,12,16,21,26,29,34,38,43,48,52,56,60,65,70,75,79,82,87,91,97,101,
%T A184917 105,110,113,119,123,128,132,136,141,145,150,154,158,164,167,172,176,
%U A184917 180,185,190,194,198,203,207,212,217,221,225,229,234,239,243,248,251,256,261,265,270,274,278,283,287,292,296,301,306,309,314,318,323,328,333,336,340,345,349,355,359,362,367,371,377,381,386,389,393,399,403,408,412,416,420,425,430,434,439,443,447,452,456,461,465,470,474,478,483,487,492,497,501,505,509,514,519,523,528,531
%N A184917 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3.
%C A184917 The sequences A184916-A184919 partition the positive integers:
%C A184917   A184916: 4,9,15,19,25,31,35,41,...
%C A184917   A184917: 3,7,12,16,21,26,29,34,...
%C A184917   A184918: 2,6,10,13,17,22,24,28,...
%C A184917   A184919: 1,5,8,11,14,18,20,23,27,...
%C A184917 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 A184917 The position of n*s in the joint ranking is
%C A184917 n+[rn/s]+[tn/s]+[un/s], and likewise for the
%C A184917 positions of n*r, n*t, and n*u.
%t A184917 r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);
%t A184917 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184917 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184917 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184917 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184917 Table[a[n],{n,1,120}]  (* A184916 *)
%t A184917 Table[b[n],{n,1,120}]  (* A184917 *)
%t A184917 Table[c[n],{n,1,120}]  (* A184918 *)
%t A184917 Table[d[n],{n,1,120}]  (* A184919 *)
%Y A184917 Cf. A184912, A184916, A184918, A184919.
%K A184917 nonn
%O A184917 1,1
%A A184917 _Clark Kimberling_, Jan 26 2011