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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?

  Submitted by DJ    
Rating: 3.7778 (9 votes)
Solution: (Hide)
Both are the sequence of perfect squares. The first is written in ternary (base 3); the second, in a quaternary (base 4) numbering system.
Decimal	Ternary	Quaternary
1	1	1
4	11	10
9	100	21
16	121	100
25	221	121
36	1100	210
49	1211	301
64	2101	1000
81	10000	1101
100	10201	1210
121	11111	1321
144	12100	2100
So, the next few terms of the first sequence are: 10000, 10201, 11111, 12100.
The next few terms of the second sequence are: 1101, 1210, 1321, 2100.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionDej Mar2007-10-29 00:44:54
No Subjectmatzerath2004-07-08 13:46:39
SequenceLarry2004-01-28 20:09:48
SOLUTIONAdy TZIDON2004-01-28 11:02:03
SolutionSolutionPenny2004-01-28 10:05:29
Solutionretiarius2004-01-28 08:41:32
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