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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A186328, A186329, A186331.

Sequence in context: A042943 A306466 A258037 * A153809 A355330 A338923

Adjacent sequences: A186327 A186328 A186329 * A186331 A186332 A186333

Keyword

nonn

Author

Clark Kimberling, Feb 17 2011

Status

approved