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A186348 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186349.

%I A186348 #14 Jul 05 2013 10:45:40
%S A186348 3,6,7,9,11,12,14,16,17,18,20,21,23,24,25,27,28,30,31,32,33,35,36,37,
%T A186348 39,40,41,42,44,45,46,48,49,50,51,52,54,55,56,57,59,60,61,62,63,65,66,
%U A186348 67,68,70,71,72,73,74,75,77,78,79,80,81,83,84,85,86,87,88
%N A186348 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2.  Complement of A186349.
%F A186348 a(n) = n+floor(sqrt(8n)).
%e A186348 First, write
%e A186348 ....8....16..24..32..40..48..56..64..72..80.. (8i)
%e A186348 1..4..9..16...25...36......49....64.......81 (squares)
%e A186348 Then replace each number by its rank, where ties are settled by ranking 8i after the square:
%e A186348 p=(3,6,7,9,11,12,14,16,17,..)=A186348=a(n).
%e A186348 q=(1,2,4,5,8,10,13,15,19,...)=A186349=n+floor((n^2-1)/8).
%t A186348 (* adjusted joint rank sequences p and q, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)
%t A186348 d=-1/2; u=8; v=0; x=1; y=0;
%t A186348 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186348 a[n_]:=n+Floor[h[n]];
%t A186348 Table[a[n],{n,1,120}]  (* A186348 *)
%o A186348 (PARI) a(n)=n+sqrtint(8*n) \\ _Charles R Greathouse IV_, Jul 05 2013
%Y A186348 Cf. A186346, A186347, A186349.
%K A186348 nonn,easy
%O A186348 1,1
%A A186348 _Clark Kimberling_, Feb 20 2011