cp's OEIS Frontend

A186275 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 octagonal numbers. Complement of A186276.

%I A186275 #4 Mar 30 2012 18:57:18
%S A186275 2,3,4,6,7,9,10,11,13,14,16,17,18,20,21,23,24,25,27,28,30,31,32,34,35,
%T A186275 37,38,39,41,42,44,45,47,48,49,51,52,54,55,56,58,59,61,62,63,65,66,68,
%U A186275 69,70,72,73,75,76,77,79,80,82,83,85,86,87,89,90,92,93,94,96,97,99,100,101,103,104,106,107,108,110,111,113,114,116,117,118,120,121,123,124,125,127,128,130,131,132,134,135,137,138,139,141
%N A186275 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 octagonal numbers.  Complement of A186276.
%C A186275 See A186159.
%e A186275 First, write the triangular and octagonal numbers:
%e A186275 1..3..6.....10..15..21..28
%e A186275 1........8..........21......
%e A186275 Then replace each by its rank, where ties are settled by ranking the triangular number after the octagonal:
%e A186275 a=(2,3,4,6,7,9,10,11,13,...)=A186275.
%e A186275 b=(1,5,8,12,15,19,22,26,...)=A186276.
%t A186275 (* adjusted joint ranking; general formula *)
%t A186275 d=-1/2; u=1/2; v=1/2; w=0; x=3; y=-2; z=0;
%t A186275 h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2);
%t A186275 a[n_]:=n+Floor[h[n]/(2x)];
%t A186275 k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2);
%t A186275 b[n_]:=n+Floor[k[n]/(2u)];
%t A186275 Table[a[n], {n, 1, 100}] (* A186275 *)
%t A186275 Table[b[n], {n, 1, 100}] (* A186276 *)
%Y A186275 Cf. A186159, A186274, A186276.
%K A186275 nonn
%O A186275 1,1
%A A186275 _Clark Kimberling_, Feb 16 2011