A186225 - OEIS

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

%S 2,3,5,6,8,9,11,13,14,16,17,19,20,22,24,25,27,28,30,32,33,35,36,38,39,

%T 41,43,44,46,47,49,50,52,54,55,57,58,60,61,63,65,66,68,69,71,73,74,76,

%U 77,79,80,82,84,85,87,88,90,91,93,95,96,98,99,101,102,104,106,107,109,110,112,114,115,117,118,120,121,123,125,126,128,129,131,132,134,136,137,139,140,142,143,145,147,148,150,151,153,155,156,158

%N 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 triangular numbers and pentagonal numbers.  Complement of A186226.

%e See A186223.

%t (* Program for adjusted rank sequences as described at A186219 *)

%t d=-1/2; u=1/2; v=1/2; w=0; x=3/2; y=-1/2; z=0; (* triangular & pentagonal *)

%t h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2);

%t a[n_]:=n+Floor[h[n]/(2x)];

%t k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2);

%t b[n_]:=n+Floor[k[n]/(2u)];

%t Table[a[n],{n,1,100}]  (* A186225 *)

%t Table[b[n],{n,1,100}]  (* A186226 *)

%Y A186219, A186223, A186224, A186226.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 15 2011