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A184915 n+[rn/u]+[sn/u]+[tn/u], where []=floor and r=2^(1/5), s=r^2, t=r^3, u=r^4. 5


%S 1,5,8,12,15,18,22,25,27,31,35,38,41,45,48,51,54,57,61,65,67,71,75,77,

%T 80,84,87,91,94,97,100,104,107,110,114,117,121,124,126,130,134,136,

%U 140,144,147,150,153,156,160,162,166,170,173,176,179,182,186,189,192,196,200,201,205,209,212,216,219,222,226,229,231,235,239,242,245,249,252,255,258,261,265,269,271,275,278,281,284,288,291,295,298,301,304,308,310,314,317,321,325,327,330,334,337,340,344,347,351,354,356,360,364,366,370,374,377,379,383,386,390,393

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

%C The sequences A184912-A184915 partition the positive integers:

%C A184912: 4,9,13,19,23,28,34,...

%C A184913: 3,7,11,16,20,24,30,...

%C A184914: 2,6,10,14,17,21,26,...

%C A184915: 1,5,8,12,15,18,22,...

%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*u in the joint ranking is

%C n+[rn/u]+[sn/u]+[tn/u], and likewise for the

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

%t r=2^(1/5); s=2^(2/5); t=2^(3/5); u=2^(4/5);

%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}] (* A184912 *)

%t Table[b[n],{n,1,120}] (* A184913 *)

%t Table[c[n],{n,1,120}] (* A184914 *)

%t Table[d[n],{n,1,120}] (* A184915 *)

%Y Cf. A184812, A184912, A184913, A184914.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 25 2011

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Last modified April 18 17:20 EDT 2019. Contains 322229 sequences. (Running on oeis4.)