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

1,1

Links

Table of n, a(n) for n=1..100.

Example

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.

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 *)

Crossrefs

Cf. A186315, A186316, A186318.

Sequence in context: A028763 A285977 A186344 * A285077 A143826 A001912

Adjacent sequences: A186314 A186315 A186316 * A186318 A186319 A186320

Keyword

nonn

Author

Clark Kimberling, Feb 17 2011

Status

approved