The following two related sequences are determined in only slightly different ways:

1
11
100
121
221
1100
1211
2101

1
10
21
100
121
210
301
1000
What the next few terms of each, and how are they determined?
(1) (1,11,100,121,221,1100,1211,2101...)
is the series of perfect squares (1,4,9,16,25,36,49,64...) in the base 3 number system. The next three terms are 10000 [81 (base 3)],
10201 [100 (base 3)], 11111 [121 (base 3)]
(2) (1,10,21,100,121,210,301,1000)
is the same series in the base 4 number system.
The next three terms are 1101 [81 (base 4)],
1210 [100 (base 4)], 1321 [121 (base 4)]
Edited on January 28, 2004, 10:34 am

Posted by Penny
on 20040128 10:05:29 