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?
The two sequences are the progression of perfect squares in different bases. Sequence '1.' is in base 3 and sequence '2. is in base 4.
As the first terms, in base 10, are 1, 4, 9, 16, 25, 36, 49, and 64, the next few terms would be 81, 100, 121, 144, 169, 196 and 225  (the sequence continuing indefinitely, but I've limited it to five digits in base 3). In sequence '1.' this would be 10000, 10201, 11111, 12100, 20021, 21021 and 22100; and, in sequence '2.' this would be 1101, 1210, 1321, 2100, 2221, 3010 and 3201.
Edited on October 29, 2007, 12:51 am

Posted by Dej Mar
on 20071029 00:44:54 