A189472 - OEIS

%I #9 Nov 16 2013 13:32:45

%S 2,5,9,11,14,18,21,23,27,30,33,36,39,43,46,48,52,55,57,61,64,67,70,73,

%T 76,80,82,86,89,92,95,98,101,105,107,110,114,116,120,123,126,129,132,

%U 135,139,141,144,148,151,153,157,160,163,166,169,173,175,178,182,185,187,191,194,197,200,203,207,210,212,216,219,221,225,228,231,234,237,241,244,246,250,253,256

%N n+[ns/r]+[nt/r]; r=1, s=e/2, t=2/e.

%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 {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are pairwise disjoint.  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=1, s=e/2, t=2/e gives

%C a=A189472, b=A189473, c=A189474.

%H Ivan Panchenko, <a href="/A189472/b189472.txt">Table of n, a(n) for n = 1..10000</a>

%t r=1; s=E/2; t=2/E;

%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}]  (*A189472*)

%t Table[b[n], {n, 1, 120}]  (*A189473*)

%t Table[c[n], {n, 1, 120}]  (*A189474*)

%Y Cf. A189473, A189474.

%K nonn

%O 1,1

%A _Clark Kimberling_, Apr 22 2011