A186328 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 pentagonal numbers and the hexagonal numbers. Complement of A186329.

1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 82, 84, 85, 87, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 112, 113, 115, 117, 119, 121, 123, 125, 126, 128, 130, 132, 134, 136, 138, 140, 141, 143, 145, 147, 149, 151, 153, 154, 156, 158, 160, 162, 164, 166, 168, 169, 171, 173, 175, 177, 179, 181, 182, 184, 186

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..5...12....22.....35......  (pentagonal)
1....6....15....28.......45.. (hexagonal)
Then replace each number by its rank, where ties are settled by ranking the pentagonal number before the hexagonal:
a=(1,3,5,7,9,11,13,15,16,....)=A186328
b=(2,4,6,8,10,12,14,17,19,...)=A186329.
		

Crossrefs

Cf. A186219, A186329, A186330, A186331,

A000384 (pentagonal), A000384 (hexagonal).

Programs

Mathematica

(* adjusted joint ranking; general formula *)
d=1/2; u=3/2; v=-1/2; 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}]  (* A186328 *)
Table[b[n], {n, 1, 100}]  (* A186329 *)