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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A186219 for a discussion of adjusted joint rank sequences.

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)

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.

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 *)

CROSSREFS

Cf. A186219, A186329, A186330, A186331,

A000384 (pentagonal), A000384 (hexagonal).

Sequence in context: A120890 A321499 A134322 * A063460 A247429 A187232

Adjacent sequences:  A186325 A186326 A186327 * A186329 A186330 A186331

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 17 2011

STATUS

approved

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Last modified May 26 05:25 EDT 2019. Contains 323579 sequences. (Running on oeis4.)