A186380 - OEIS

%I #4 Mar 30 2012 18:57:18

%S 1,2,4,6,8,11,14,17,20,23,27,31,35,40,45,50,55,60,66,72,78,85,92,99,

%T 106,113,121,129,137,146,155,164,173,182,192,202,212,223,234,245,256,

%U 267,279,291,303,316,329,342,355,368,382,396,410,425,440,455,470,485,501,517,533,550,567,584,601,618,636,654,672,691,710,729,748,767,787,807,827,848,869,890,911,932,954,976,998,1021,1044

%N Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number).  Complement of A186379.

%C See A186379.

%F a(n)=n+floor(-1/2+sqrt(8n-3/4))=A186379(n).

%F b(n)=n+floor((n^2+n+1)/8)=A186380(n).

%e First, write

%e .....4..8..12..16..20..24..28.. (4*i)

%e 1..3..6..10..15.....21.....28.. (triangular)

%e Then replace each number by its rank, where ties are settled by ranking 4i before the triangular:

%e a=(3,5,7,9,10,12,13,15,16,..)=A186379

%e b=(1,2,4,6,8,11,14,17,20,...)=A186380.

%t (See A186379.)

%Y Cf. A186379, A186381, A186382.

%K nonn

%O 1,2

%A _Clark Kimberling_, Feb 19 2011