Cantor Expressions: Solving A-F (2,7,19,87,1000,1M)

[raross]

What is the cantor expansion of:

A. 2
B. 7
C. 19
D. 87
E. 1000
F. 1,000,000

The algorithm to solve these small problems is the most difficult for me.
The algorithm that I came up with states:
Asub(n) N! + Asub(n-1) (n-1)! +...+ Asub(2)2! + Asub(1)1!, where
Asub1 is an integer with 0 <= Asubi <= i for i = 1,2,...n,

I have tried to find other information on google, and have failed. It seems there is not much help with cantor expressions. So any help would be grateful!

 

[EnumaElish]

Have you seen http://www.rose-hulman.edu/mathjournal/2004/vol5-n1/paper4/v5n1-4do.doc ?

2.2 Example
23 = 3*3!+2*2!+1*1!
24 = 23 + 1 = 3*3!+2*2!+1*1! + 1 = 4!

This has an algorithm to convert a decimal number to Cantor.

 

[raross]

So do these answers make sense or am I doing it wrong?

2 = 1*1! + 1
7 = 2*2! + 1*1! + 2
19 = 2*2! + 1*1! + 14
87 = 3*3! + 2*2! + 1*1! + 64


Thanks for your help!

 

[raross]

Im not sure how many digits you can put at the end, but it only makes sense I guess. Anyone help?

 

[raross]

2 = 1*1! + 1
7 = 2*2! + 1*1! + 2
19 = 3*3! + 1
87 = 4*4! - 9

Hrmm, how about these answers?
Anyone have a clue?