cp's OEIS Frontend

A186353 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186353.

%I A186353 #4 Mar 30 2012 18:57:18
%S A186353 1,3,6,9,12,16,21,26,31,37,44,51,58,66,75,84,93,103,114,125,136,148,
%T A186353 161,174,187,201,216,231,246,262,279,296,313,331,350,369,388,408,429,
%U A186353 450,471,493,516,539,562,586,611,636,661,687,714,741,768,796,825,854,883,913,944,975,1006,1038,1071,1104,1137,1171,1206,1241,1276,1312,1349,1386,1423,1461,1500,1539,1578,1618,1659,1700,1741,1783,1826,1869,1912,1956,2001,2046,2091
%N A186353 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers.  Complement of A186353.
%F A186353 a(n)=n+floor(-1/2+sqrt(4n-3/4))=A186352(n).
%F A186353 b(n)=n+floor((n^2+n+1)/4)=A186353(n).
%e A186353 First, write
%e A186353 1..3..5..7..9..11..13..15..17..21..23.. (odds)
%e A186353 1..3....6.....10.......15......21.... (triangular)
%e A186353 Then replace each number by its rank, where ties are settled by ranking the odd number after the triangular:
%e A186353 a=(2,4,5,7,8,10,11,13,14,15,....)=A186352
%e A186353 b=(1,3,6,9,12,16,21,26,31,37,...)=A186353.
%t A186353 (See A186352.)
%Y A186353 Cf. A186350, A186351, A186352.
%K A186353 nonn
%O A186353 1,2
%A A186353 _Clark Kimberling_, Feb 18 2011