cp's OEIS Frontend

A186387 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186388.

%I A186387 #7 Mar 30 2012 18:57:18
%S A186387 3,6,8,10,12,13,15,17,18,20,21,23,24,26,27,29,30,32,33,34,36,37,39,40,
%T A186387 41,43,44,45,47,48,49,51,52,53,54,56,57,58,60,61,62,63,65,66,67,68,70,
%U A186387 71,72,73,75,76,77,78,80,81,82,83,85,86,87,88,89,91,92
%N A186387 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number).  Complement of A186388.
%C A186387 See A186350 for a discussion of adjusted joint rank sequences.
%e A186387 First, write
%e A186387 ......6.....12..18....24..30. (6*i)
%e A186387 1..3..6..10...15....21..28... (triangular)
%e A186387 Then replace each number by its rank, where ties are settled by ranking 6i before the triangular:
%e A186387 a=(3,6,8,10,12,13,15,17,...)=A186387
%e A186387 b=(1,2,4,5,7,9,11,14,16,...)=A186388.
%t A186387 (* 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 A186387 d=1/2; u=6; v=0; x=1/2; y=1/2; (* 6i and triangular *)
%t A186387 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186387 a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *)
%t A186387 k[n_]:=(x*n^2+y*n-v+d)/u;
%t A186387 b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *)
%t A186387 Table[a[n], {n, 1, 120}]  (* A186387 *)
%t A186387 Table[b[n], {n, 1, 100}]  (* A186388 *)
%Y A186387 Cf. A186350, A186388, A186389, A186390.
%K A186387 nonn
%O A186387 1,1
%A A186387 _Clark Kimberling_, Feb 19 2011