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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. 4
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 (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..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.

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 *)

CROSSREFS

Cf. A186219, A186325, A186326, A186327,

A000290 (squares), A000567 (octagonal).

Sequence in context: A089585 A121506 A114119 * A101358 A276210 A186223

Adjacent sequences:  A186321 A186322 A186323 * A186325 A186326 A186327

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 17 2011

STATUS

approved

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Last modified May 22 19:19 EDT 2019. Contains 323481 sequences. (Running on oeis4.)