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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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Solution Solution Comment 6 of 6 |

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 2007-10-29 00:44:54

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