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

1. 1
   11
   100
   121
   221
   1100
   1211
   2101
   

2. 1
   10
   21
   100
   121
   210
   301
   1000
   

What the next few terms of each, and how are they determined?

I noticed that 121 shows up in both these lists, and is also a square in base 10.  Quick calculations showed that it's a square in base 5 (36) and 6 (49) as well.  Of course, it should have occurred to me before: 121 base B = B^2 + 2B + 1 = (B + 1)^2, so 121 is a square in every base >=3.  Cute.

Posted by matzerath on 2004-07-08 13:46:39