A186330 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 pentagonal numbers and the hexagonal numbers. Complement of A186331.

2, 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

Does this differ (apart from a(1)) from A186329 or A186328? - R. J. Mathar, Feb 25 2011

Examples

			First, write
1..5...12....22.....35......  (pentagonal)
1....6....15....28.......45.. (hexagonal)
Replace each number by its rank, where ties are settled by ranking the pentagonl number after the hexagonal:
a=(1,3,5,7,9,11,13,15,16,....)=A186330
b=(2,4,6,8,10,12,14,17,19,...)=A186331.
		

Crossrefs

Cf. A186328, A186329, A186331.

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}]  (* A186330 *)
Table[b[n], {n, 1, 100}]  (* A186331 *)