cp's OEIS Frontend

A186516 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2. Complement of A186515.

%I A186516 #5 Mar 30 2012 18:57:19
%S A186516 3,6,9,13,16,19,22,25,29,32,35,38,42,45,48,51,55,58,61,64,67,71,74,77,
%T A186516 80,84,87,90,93,97,100,103,106,110,113,116,119,122,126,129,132,135,
%U A186516 139,142,145,148,152,155,158,161,165,168,171,174,177,181,184,187,190,194,197,200,203,207,210,213,216,220,223,226,229,233,236,239,242,245,249,252,255,258,262,265,268,271
%N A186516 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2.  Complement of A186515.
%C A186516 See A186219 for a discussion of adjusted joint rank sequences.
%C A186516 The pairs (i,j) for which i^2=4+5j^2 are (L(2h),F(2h)), where L=A000032 (Lucas numbers) and F=A000045 (Fibonacci numbers).
%F A186516 a(n)=n+floor(sqrt((n^2)/5-7/10))=A186515(n).
%F A186516 b(n)=n+floor(sqrt(5n^2+7/2))=A186516(n).
%e A186516 First, write
%e A186516 1..4..9..16..25..36..49.. (i^2)
%e A186516 ......9.....24.......49.. (4+5j^2)
%e A186516 Then replace each number by its rank, where ties are settled by ranking i^2 after 4+5j^2:
%e A186516 a=(1,2,4,5,7,8,10,11,12,14,15,17,..)=A186515
%e A186516 b=(3,6,9,13,16,19,22,25,29,32,35,..)=A186516.
%t A186516 (See A186515.)
%Y A186516 Cf. A186219, A186513, A186514, A186515.
%K A186516 nonn
%O A186516 1,1
%A A186516 _Clark Kimberling_, Feb 22 2011