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Basic Concepts (Posted on 2004-01-28) Difficulty: 3 of 5
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?

See The Solution Submitted by DJ    
Rating: 3.7778 (9 votes)

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No Subject | Comment 5 of 6 |
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
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