A186317 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 squares and hexagonal numbers. Complement of A186318.

2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 83, 85, 87, 89, 90, 92, 94, 95, 97, 99, 100, 102, 104, 106, 107, 109, 111, 112, 114, 116, 118, 119, 121, 123, 124, 126, 128, 129, 131, 133, 135, 136, 138, 140, 141, 143, 145, 147, 148, 150, 152, 153, 155, 157, 159, 160, 162, 164, 165, 167, 169, 170

Offset: 1

Author

Clark Kimberling, Feb 17 2011

Keywords

• nonn

Examples

			First, write
1..4...9...16..25....36....49. (squares)
1....6...15.......28....45.... (hexagonals)
Replace each number by its rank, where ties are settled by ranking the square number after the hexagonal:
a=(2,3,5,7,8,10,12,13,...)=A186317.
b=(1,4,6,9,11,14,16,18,...)=A186318.
		

Crossrefs

Cf. A186315, A186316, A186318.

Programs

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/2; u=1; v=0; w=0; x=2; y=-1; z=0;
h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2);
a[n_]:=n+Floor[h[n]/(2x)];
k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2);
b[n_]:=n+Floor[k[n]/(2u)];
Table[a[n], {n, 1, 100}]  (* A186317 *)
Table[b[n], {n, 1, 100}]  (* A186318 *)