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

%I #4 Mar 30 2012 18:57:17

%S 2,6,10,13,17,22,24,28,32,36,40,44,47,50,54,59,63,66,69,73,76,81,85,

%T 88,92,95,100,103,107,111,114,118,122,126,129,133,138,140,144,148,151,

%U 155,160,163,166,170,174,178,182,186,189,192,197,201,204,208,211,215,219,223,227,230,233,238,241,245,249,253,257,260,264,267,271,276,280,282,286,290,293,298,302,304,308,312,317,320,324,327,330,335,339,343,346,350,353,357,361,365,369,372,376,380,383,387,391,395,398,402,406,409,414,418,421,424,428,432,436,440,444,446

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

%C The sequences A184916-A184919 partition the positive integers:

%C A184916: 4,9,15,19,25,31,35,41,...

%C A184917: 3,7,12,16,21,26,29,34,...

%C A184918: 2,6,10,13,17,22,24,28,...

%C A184919: 1,5,8,11,14,18,20,23,27,...

%C 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 The position of n*t in the joint ranking is

%C n+[rn/t]+[sn/t]+[un/t], and likewise for the

%C positions of n*r, n*s, and n*u.

%t r=1; s=2^(1/4); t=2^(1/2); u=2^(3/4);

%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}] (* A184916 *)

%t Table[b[n],{n,1,120}] (* A184917 *)

%t Table[c[n],{n,1,120}] (* A184918 *)

%t Table[d[n],{n,1,120}] (* A184919 *)

%Y Cf. A184912, A184916, A184917, A184919.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 26 2011

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