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A186346 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186347.

%I A186346 #5 Mar 30 2012 18:57:18
%S A186346 3,5,7,9,11,12,14,15,17,18,20,21,23,24,25,27,28,29,31,32,33,35,36,37,
%T A186346 39,40,41,42,44,45,46,47,49,50,51,52,54,55,56,57,59,60,61,62,63,65,66,
%U A186346 67,68,69,71,72,73,74,75,77,78,79,80,81,83,84,85,86,87,88,90,91,92,93,94,95,97,98,99,100,101,102,104,105,106,107,108,109,111,112,113,114,115,116,117,119,120,121,122,123,124,125,127,128,129,130,131,132,133,135,136,137,138,139,140,141
%N A186346 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2.  Complement of A186347.
%C A186346 See A186350 for a discussion of adjusted joint rank sequences.
%F A186346 a(n)=n+floor(sqrt(8n-1/2))=A186346(n).
%F A186346 b(n)=n+floor((n^2+1/2)/8)=A186347(n).
%e A186346 First, write
%e A186346 ....8....16..24..32..40..48..56..64..72..80.. (8i)
%e A186346 1..4..9..16...25...36......49....64.......81 (squares)
%e A186346 Then replace each number by its rank, where ties are settled by ranking 8i before the square:
%e A186346 a=(3,5,7,9,11,12,14,15,17,..)=A186346
%e A186346 b=(1,2,4,6,8,10,13,16,19,...)=A186347.
%t A186346 (* adjusted joint rank sequences a and b, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)
%t A186346  d=1/2; u=8; v=0; x=1; y=0;
%t A186346 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186346 a[n_]:=n+Floor[h[n]];
%t A186346 k[n_]:=(x*n^2+y*n-v+d)/u;
%t A186346 b[n_]:=n+Floor[k[n]];
%t A186346 Table[a[n],{n,1,120}]  (* A186346 *)
%t A186346 Table[b[n],{n,1,100}]  (* A186347 *)
%Y A186346 Cf. A186350, A186347, A186348, A186349.
%K A186346 nonn
%O A186346 1,1
%A A186346 _Clark Kimberling_, Feb 20 2011