A182801 - OEIS

A182801

Joint-rank array of the numbers j*r^(i-1), where r = golden ratio = (1+sqrt(5))/2, i>=1, j>=1, read by antidiagonals.

1, 3, 2, 5, 6, 4, 7, 9, 11, 8, 10, 13, 16, 19, 14, 12, 18, 23, 28, 32, 25, 15, 21, 31, 39, 48, 54, 42, 17, 26, 36, 52, 66, 81, 89, 71, 20, 29, 44, 61, 86, 110, 134, 147, 117, 22, 34, 49, 73, 102, 141, 181, 221, 240, 193, 24, 38, 57, 82

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Joint-rank arrays are introduced here as follows.

Suppose that R={f(i,j)} is set of positive numbers, where i and j range through countable sets I and J, respectively, such that for every n, then number f(i,j) < n is finite. Let T(i,j) be the position of f(i,j) in the joint ranking of all the numbers in R. The joint-rank array of R is the array T whose i-th row is T(i,j).

For A182801, f(i,j)=j*r^(i-1), where r=(1+sqrt(5))/2 and I=J={1,2,3,...}.

(row 1)=A020959; (row 2)=A020960; (row 3)=A020961.

(col 1)=A020956; (col 2)=A020957; (col 3)=A020958.

Every positive integer occurs exactly once in A182801, so that as a sequence it is a permutation of the positive integers.

LINKS

Table of n, a(n) for n=1..59.

FORMULA

T(i,j)=Sum{floor(j*r^(i-k)): k>=1}.

EXAMPLE

Northwest corner:

1....3....5....7...10...12...

2....6....9...13...18...21...