cp's OEIS Frontend

A186389 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186390.

%I A186389 #6 Mar 30 2012 18:57:18
%S A186389 4,6,8,10,12,14,15,17,18,20,22,23,25,26,27,29,30,32,33,35,36,37,39,40,
%T A186389 41,43,44,45,47,48,49,51,52,53,55,56,57,58,60,61,62,63,65,66,67,69,70,
%U A186389 71,72,74,75,76,77,78,80,81,82,83,85,86,87,88,90,91,92
%N A186389 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number).  Complement of A186390.
%C A186389 See A186350 for a discussion of adjusted joint rank sequences.
%e A186389 First, write
%e A186389 ......6.....12..18....24..30. (6i)
%e A186389 1..3..6..10...15....21..28... (triangular)
%e A186389 Then replace each number by its rank, where ties are settled by ranking 6i after the triangular:
%e A186389 a=(4,6,8,10,12,14,15,17,...)=A186389
%e A186389 b=(1,2,3,5,7,9,11,13,16,...)=A186390.
%t A186389 (* adjusted joint rank sequences a and b, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)
%t A186389 d=-1/2; u=6; v=0; x=1/2; y=1/2; (* 6i and triangular *)
%t A186389 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186389 a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *)
%t A186389 k[n_]:=(x*n^2+y*n-v+d)/u;
%t A186389 b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *)
%t A186389 Table[a[n], {n, 1, 120}]  (* A186389 *)
%t A186389 Table[b[n], {n, 1, 100}]  (* A186390 *)
%Y A186389 Cf. A186350, A186387, A186388, A186390.
%K A186389 nonn
%O A186389 1,1
%A A186389 _Clark Kimberling_, Feb 19 2011