A184926 - OEIS

%I #6 Mar 30 2012 18:57:17

%S 2,5,9,12,15,19,23,26,29,32,36,40,43,46,49,53,57,60,63,66,70,74,77,80,

%T 84,87,90,94,97,101,104,107,111,115,118,121,124,127,132,134,138,141,

%U 145,149,152,155,159,162,164,169,172,176,179,182,186,190,193,195,199,202,207,210,213,216,220,224,226,230,233,237,240,244,247,251,254,256,261,264,268,270,274,278,282,285,288,291,294,299,301,305,308,312,316,319,322,325,329,331,336,339,343,346,349,353,356,360,362,366,369,374,376,380,383,386,391,393,397,400,404,406

%N n+[rn/t]+[sn/t]+[un/t], 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*t in the joint ranking is n+[rn/t]+[sn/t]+[un/t], and likewise for the positions of n*r, n*s, 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. A184924, A184925, A184927.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 26 2011