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%I #6 Mar 30 2012 18:57:17
%S 6,14,21,28,37,44,52,59,67,75,83,89,98,106,112,120,128,136,143,150,
%T 158,167,173,181,189,197,204,212,219,227,235,242,250,257,265,273,280,
%U 287,296,303,311,318,326,334,341,348,357,364,371,379,387,395,402,409,417,425,432,440,448,455,463,471,478,486,493,501,509,516,524,532,538,546,555,562,569,577,585,593,600,607,616,623,630,638,646,653,661,668,677,684,691,699,707,714,722,729,737,745,752,760,767,775,783,791,797,806,814,821,828,836,844,851,858,866,875,881,889,897,905,912
%N n+[sn/r]+[tn/r]+[un/r], where []=floor and r=1, s=sqrt(3), t=sqrt(5), u=sqrt(7).
%C The sequences A184924-A184927 partition the positive integers:
%C A184924: 6,14,21,28,37,44,52,59,...
%C A184925: 3,8,11,17,20,25,30,34,...
%C A184926: 2,5,9,12,15,19,23,26,29,...
%C A184927: 1,4,7,10,13,16,18,22,24,...
%C Jointly rank the sets {h*r}, {i*s}, {j*t}, {k*u},
%C where 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.
%t r=1; s=3^(1/2); t=5^(1/2); u=7^(1/2);
%t a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t Table[a[n],{n,1,120}] (* A184924 *)
%t Table[b[n],{n,1,120}] (* A184925 *)
%t Table[c[n],{n,1,120}] (* A184926 *)
%t Table[d[n],{n,1,120}] (* A184927 *)
%Y Cf. A184912, A184916, A184920, A184925, A184926, A184927.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 26 2011