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 A184916 n+[sn/r]+[tn/r]+[un/r], where []=floor and r=1, s=2^(1/4), t=s^2, u=s^3. 7

%I #5 Mar 30 2012 18:57:17

%S 4,9,15,19,25,31,35,41,46,51,57,62,67,72,78,83,89,94,98,104,109,115,

%T 120,125,131,135,142,147,152,157,162,168,173,179,183,188,195,199,205,

%U 210,214,220,226,231,236,242,247,252,258,263,268,273,279,284,289,295,299,305,311,315,321,326,331,337,342,347,352,358,364,368,374,379,384,390,396,400,405,411,415,422,427,431,437,442,448,453,459,463,468,475,480,485,490,495,500,506,512,516,522,527,532,538,543,548,553,559,564,569,575,579,585,591,596,601,606,612,617,622,628,632

%N n+[sn/r]+[tn/r]+[un/r], 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*r in the joint ranking is

%C n+[sn/r]+[tn/r]+[un/r], and likewise for the

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

%F a(n)=n+[sn/r]+[tn/r]+[un/r], where []=floor and

%F r=1, s=2^(1/4), t=s^2, u=s^3.

%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, A184917, A184918, A184919.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 26 2011

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