cp's OEIS Frontend

A186540 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)=-2+3j^2. Complement of A186539.

%I A186540 #12 Feb 12 2025 05:47:05
%S A186540 2,5,8,10,13,16,19,21,24,27,30,32,35,38,40,43,46,49,51,54,57,60,62,65,
%T A186540 68,71,73,76,79,81,84,87,90,92,95,98,101,103,106,109,112,114,117,120,
%U A186540 122,125,128,131,133,136,139,142,144,147,150,152,155,158,161,163,166,169,172,174,177,180,183,185,188,191,193,196,199,202,204,207,210,213,215,218
%N A186540 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)=-2+3j^2. Complement of A186539.
%C A186540 See A186219 for a discussion of adjusted joint rank sequences.
%C A186540 Does this differ from A054088? The first 42000 entries of both sequences at least are the same. - _R. J. Mathar_, Feb 25 2011
%F A186540 b(n) = n+floor(sqrt((1/3)n^2+1/24)) = A186539(n).
%F A186540 a(n) = n+floor(sqrt(3n^2-3/2)).
%e A186540 First, write
%e A186540 1..4..9..16..25..36..49.. (i^2)
%e A186540 .......10....25....46.. (-2+3j^2)
%e A186540 Then replace each number by its rank, where ties are settled by ranking i^2 before -2+3j^2:
%e A186540 b=(1,3,4,6,7,9,11,12,14,15,17,18,..)=A186539
%e A186540 a=(2,5,8,10,13,16,19,21,24,27,30...).
%t A186540 (* See A186539 *)
%Y A186540 Cf. A186219, A186539, A186541, A186542.
%K A186540 nonn
%O A186540 1,1
%A A186540 _Clark Kimberling_, Feb 23 2011