cp's OEIS Frontend

A186385 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186386.

%I A186385 #6 Mar 30 2012 18:57:18
%S A186385 3,6,8,9,11,13,14,16,18,19,21,22,23,25,26,28,29,30,32,33,35,36,37,39,
%T A186385 40,41,42,44,45,46,48,49,50,51,53,54,55,57,58,59,60,62,63,64,65,66,68,
%U A186385 69,70,71,73,74,75,76,77,79,80,81,82,84,85,86,87,88,90,91
%N A186385 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number).  Complement of A186386.
%e A186385 First, write
%e A186385 .....5...10..15..20..25..30.. (5*i)
%e A186385 1..3..6..10..15....21..28.. (triangular)
%e A186385 Then replace each number by its rank, where ties are settled by ranking 5*i after the triangular:
%e A186385 a=(3,6,8,9,11,13,14,16,18,..)=A186385
%e A186385 b=(1,2,4,5,7,10,12,15,17,...)=A186386.
%t A186385 (* 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 A186385 d=-1/2; u=5; v=0; x=1/2; y=1/2; (* 5i and triangular *)
%t A186385 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186385 a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *)
%t A186385 k[n_]:=(x*n^2+y*n-v+d)/u;
%t A186385 b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *)
%t A186385 Table[a[n], {n, 1, 120}]  (* A186385 *)
%t A186385 Table[b[n], {n, 1, 100}]  (* A186386 *)
%Y A186385 Cf. A186350, A186383, A186384, A186386.
%K A186385 nonn
%O A186385 1,1
%A A186385 _Clark Kimberling_, Feb 19 2011