cp's OEIS Frontend

A186500 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2. Complement of A186499.

%I A186500 #6 Mar 30 2012 18:57:19
%S A186500 2,6,9,12,16,19,22,25,29,32,35,38,42,45,48,51,54,58,61,64,67,71,74,77,
%T A186500 80,84,87,90,93,97,100,103,106,110,113,116,119,122,126,129,132,135,
%U A186500 139,142,145,148,152,155,158,161,165,168,171,174,177,181,184,187,190,194,197,200,203,207,210,213,216,220,223,226,229,232,236,239,242,245,249,252,255,258,262,265
%N A186500 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2.  Complement of A186499.
%C A186500 See A186219 for a discussion of adjusted joint rank sequences.
%C A186500 The pairs (i,j) for which i^2=-4+5j^2 are (L(2h-2),F(2h-1)), where L=A000032 (Lucas numbers) and F=A000045 (Fibonacci numbers).
%F A186500 a(n)=n+floor((1/10)(sqrt(2n^2+7)))=A186499(n).
%F A186500 b(n)=n+floor(sqrt(5n^2-7/2))=A186500(n).
%e A186500 First, write
%e A186500 1..4..9..16..25..36..49..... (i^2)
%e A186500 1........16........41........(-4+5j^2)
%e A186500 Then replace each number by its rank, where ties are settled by ranking i^2 before -4+5j^2:
%e A186500 a=(1,3,4,5,7,8,10,11,13,14,15,17,18...)=A186499
%e A186500 b=(2,6,9,12,16,19,22,25,29,32,35,38,.)=A186500.
%t A186500 (See A186499.)
%Y A186500 Cf. A186219, A186499, A186511, A186512.
%K A186500 nonn
%O A186500 1,1
%A A186500 _Clark Kimberling_, Feb 22 2011