A186324 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186325.

1, 3, 5, 6, 8, 9, 11, 12, 14, 16, 17, 19, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36, 38, 39, 41, 42, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 94, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 113, 115, 117, 118, 120, 121, 123, 124, 126, 128, 129, 131, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 151, 153, 154, 156, 158

Offset: 1

Author

Clark Kimberling, Feb 17 2011

Keywords

• nonn

Comments

See A186219 for a discussion of adjusted joint rank sequences.

Examples

			First, write
1..4...9..16....25..36....49..64...  (squares)
1....8.......21........40........65. (octagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the octagonal:
a=(1,3,5,6,8,9,11,12,14,...)=A186324
b=(2,4,7,10,13,15,18,21,...)=A186325.
		

Crossrefs

Cf. A186219, A186325, A186326, A186327,

A000290 (squares), A000567 (octagonal).

Programs

Mathematica

(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; w=0; x=3; y=-2; 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}]  (* A186324 *)
Table[b[n], {n, 1, 100}]  (* A186325 *)