perplexus.info :: Sequences : Basic Concepts

Basic Concepts (Posted on 2004-01-28)

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?

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
Puzzle Thoughts	K Sengupta	2024-01-09 11:48:39
Solution	Dej Mar	2007-10-29 00:44:54
No Subject	matzerath	2004-07-08 13:46:39
Sequence	Larry	2004-01-28 20:09:48
SOLUTION	Ady TZIDON	2004-01-28 11:02:03
Solution	Penny	2004-01-28 10:05:29
Solution	retiarius	2004-01-28 08:41:32

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