Continued thoughts on n-White numbers

[James A. Sellers]

I was intrigued with all the previous email on n-White numbers, especially the brief pattern mentioned in one of the emails which discussed certain n-White numbers:

n=1, 1-White number = 9
n=2, 2-White number = 99
n=3, 3-White number = 1999
n=4, 4-White number = 19999

It turns out that this table can be extended, but does not appear to allow for "infinite" extension.

n=5, 5-White number = 299998 = 3*10^5 - 2
n=6, 6-White number = 2999998 = 3*10^6 - 2
n=7, 7-White number = 39999997 = 4*10^7 -3
n=8, 8-White number = 399999997 = 4*10^8 -3
n=9, 9-White number = 4999999996 = 5*10^9 -4
n=10, 10-White number = 49999999996 = 5*10^10 -4
n=11, 11-White number = 599999999995 = 6*10^11 -5
n=12, 12-White number = 5999999999995 = 6*10^12 -5

This pattern continues for n=13 and 14, but appears to end there.  As a matter of fact, at n=16, I looked for a 16-White number between 8*10^16-100 and 8*10^16+100 with no success.  UGH!!!!  

Anyway, just thought I would mention this finite extension of the pattern mentioned in the previous email.  Thanks for your time.

James



****************************************
James A. Sellers
Associate Professor, Mathematics
Cedarville College

sellersj at cedarville.edu
http://www.cedarville.edu/dept/sm/jas_www.htm