cp's OEIS Frontend

A184913 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.

%I A184913 #5 Mar 30 2012 18:57:17
%S A184913 3,7,11,16,20,24,30,33,37,42,46,50,55,60,64,68,72,76,81,85,90,95,99,
%T A184913 102,106,111,116,120,125,129,132,137,141,146,151,155,159,164,167,171,
%U A184913 177,181,185,190,194,198,202,207,211,215,220,224,228,234,237,241,246,250,254,259,264,267,272,276,280,285,289,294,299,302,306,311,315,320,324,329,333,336,341,345,350,355,359,363,367,371,375,381,385,389,394,398,401,406,411,415,419,424,428,432,437,441,445,450,454,458,463,468,471,476,480,484,489,493,498,502,506,510,515,519
%N A184913 n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4.
%C A184913 The sequences A184912-A184915 partition the positive integers:
%C A184913   A184912: 4,9,13,19,23,28,34,...
%C A184913   A184913: 3,7,11,16,20,24,30,...
%C A184913   A184914: 2,6,10,14,17,21,26,...
%C A184913   A184915: 1,5,8,12,15,18,22,...
%C A184913 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 A184913 The position of n*s in the joint ranking is
%C A184913 n+[rn/s]+[tn/s]+[un/s], and likewise for the
%C A184913 positions of n*r, n*t, and n*u.
%t A184913 r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);
%t A184913 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r]+Floor[n*u/r];
%t A184913 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s]+Floor[n*u/s];
%t A184913 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]+Floor[n*u/t];
%t A184913 d[n_]:=n+Floor[n*r/u]+Floor[n*s/u]+Floor[n*t/u];
%t A184913 Table[a[n],{n,1,120}]  (* A184912 *)
%t A184913 Table[b[n],{n,1,120}]  (* A184913 *)
%t A184913 Table[c[n],{n,1,120}]  (* A184914 *)
%t A184913 Table[d[n],{n,1,120}]  (* A184915 *)
%Y A184913 Cf. A184812, A184913, A184914, A184915.
%K A184913 nonn
%O A184913 1,1
%A A184913 _Clark Kimberling_, Jan 25 2011