A184871 - OEIS

%I #9 Sep 04 2015 10:32:10

%S 4,9,13,19,23,28,34,38,43,48,53,58,63,68,72,78,82,87,93,97,102,107,

%T 112,117,122,127,131,137,141,146,151,156,161,165,171,176,180,186,190,

%U 195,200,205,210,215,220,224,230,235,239,245,249,254,260,264,269,274,279,283,288,294,298,303,308,313,318,323,328,332,338,342,347,353,357,362,367,372,377,382,387,391,397,401,406,412,416,421,426,431,436,440,446,450,455,460,465,470,475,480,484,490,495,499,505,509,514,520,524,529,534,539,543,549,554,558,564,568,573,578,583,588

%N n+floor(ns/r)+floor(nt/r), where r=log(2), s=log(3), t=log(5).

%C This is one of three sequences that partition the positive integers.  In general, suppose that r, s, t are positive real numbers for which the sets

%C {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are disjoint.

%C Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked.  Define b(n) and c(n) as the ranks of n/s and n/t.  It is easy to prove that

%C a(n)=n+[ns/r]+[nt/r],

%C b(n)=n+[nr/s]+[nt/s],

%C c(n)=n+[nr/t]+[ns/t], where []=floor.

%C Taking r=log(2), s=log(3), t=log(5) yields

%C a=A184871, b=A184872, c=A184873.

%t r=Log[2]; s=Log[3]; t=Log[5];

%t a[n_]:=n+Floor [n*s/r]+Floor[n*t/r];

%t b[n_]:=n+Floor [n*r/s]+Floor[n*t/s];

%t c[n_]:=n+Floor[n*r/t]+Floor[n*s/t];

%t Table[a[n],{n,1,120}]  (* A184871 *)

%t Table[b[n],{n,1,120}]  (* A184872 *)

%t Table[c[n],{n,1,120}]  (* A184873 *)

%Y Cf. A184812, A184872, A184873, A184874 (primes in A184872).

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 23 2011

%E Name corrected by _Charles R Greathouse IV_, Sep 04 2015