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.

3, 6, 7, 9, 11, 12, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88

Offset: 1

Author

Clark Kimberling, Feb 20 2011

Keywords

• nonn
• easy

Examples

			First, write
....8....16..24..32..40..48..56..64..72..80.. (8i)
1..4..9..16...25...36......49....64.......81 (squares)
Then replace each number by its rank, where ties are settled by ranking 8i after the square:
p=(3,6,7,9,11,12,14,16,17,..)=A186348=a(n).
q=(1,2,4,5,8,10,13,15,19,...)=A186349=n+floor((n^2-1)/8).
		

Crossrefs

Cf. A186346, A186347, A186349.

Programs

Mathematica

(* 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 *)
d=-1/2; u=8; v=0; x=1; y=0;
h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
a[n_]:=n+Floor[h[n]];
Table[a[n],{n,1,120}]  (* A186348 *)

PARI

a(n)=n+sqrtint(8*n) \\ Charles R Greathouse IV, Jul 05 2013

Formula

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