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A184921 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3. 4


%S 3,8,13,18,23,27,32,37,42,47,52,56,61,66,71,76,81,85,90,95,100,105,

%T 110,114,119,124,129,134,139,143,148,153,158,163,167,172,177,182,187,

%U 192,196,201,206,211,216,221,225,230,235,240,245,250,254,259,264,269,274,279,283,288,293,298,303,308,312,317,322,327,332,336,341,346,351,356,361,365,370,375,380,385,390,394,399,404,409,414,419,423,428,433,438,443,448,452,457,462,467,472,477,481,486,491,496,501,505,510,515,520,525,530,534,539,544,549,554,559,563,568,573,578

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

%C The sequences A184920-A184923 partition the positive integers:

%C A184920: 7,15,24,31,40,48,55,64,...

%C A184921: 3,8,13,18,23,27,32,37,...

%C A184922: 2,5,9,12,16,19,22,26,29,...

%C A184923: 1,4,6,10,11,14,17,20,21,...

%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*s in the joint ranking is n+[rn/s]+[tn/s]+[un/s], and likewise for the positions of n*r, n*t, and n*u.

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

%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}] (* A184920 *)

%t Table[b[n],{n,1,120}] (* A184921 *)

%t Table[c[n],{n,1,120}] (* A184922 *)

%t Table[d[n],{n,1,120}] (* A184923 *)

%Y Cf. A184912, A184920, A184922, A184923.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 26 2011

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