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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. 4

%I

%S 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 39,40,41,42,44,45,46,48,49,50,51,52,54,55,56,57,59,60,61,62,63,65,66,

%U 67,68,70,71,72,73,74,75,77,78,79,80,81,83,84,85,86,87,88

%N 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 a(n) = n+floor(sqrt(8n)).

%e First, write

%e ....8....16..24..32..40..48..56..64..72..80.. (8i)

%e 1..4..9..16...25...36......49....64.......81 (squares)

%e Then replace each number by its rank, where ties are settled by ranking 8i after the square:

%e p=(3,6,7,9,11,12,14,16,17,..)=A186348=a(n).

%e q=(1,2,4,5,8,10,13,15,19,...)=A186349=n+floor((n^2-1)/8).

%t (* 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 d=-1/2; u=8; v=0; x=1; y=0;

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

%t a[n_]:=n+Floor[h[n]];

%t Table[a[n],{n,1,120}] (* A186348 *)

%o (PARI) a(n)=n+sqrtint(8*n) \\ _Charles R Greathouse IV_, Jul 05 2013

%Y Cf. A186346, A186347, A186349.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Feb 20 2011

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Last modified May 23 13:32 EDT 2019. Contains 323514 sequences. (Running on oeis4.)