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 Pair formed Sequence (Posted on 2007-02-09)
Find the rule or give the next few terms to this sequence.

6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38...

 See The Solution Submitted by Jer Rating: 4.0000 (1 votes)

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 Puzzle Solution Comment 6 of 6 |

The sequence corresponds to the product a*b of two distinct prime numbers a and b, such that the said products a*b are arranged in ascending order of magnitude .

For example:

2*3 = 6
2*5 = 10
2*7 = 14
3*5 = 15, and so on, until:
2*19 = 38

Now, we observe that:

3*13 = 39
2*23 = 46
3*17 = 51
5*11 = 55
3*19 = 57
2*29 = 58
2*31 = 62
5*13 = 65

Consequently, the next eight numbers are 39, 46, 51, 55, 57, 58, 62 and 65

Notes:

(i) Of course, there exists many other terms apart from just the eight mentioned above.

(ii) Numbers like 27 and 60 cannot be included in the given sequence, since either these numbers are prime powers or at least one of a and b is a prime power, and therefore composite.

Edited on April 4, 2008, 6:18 am
 Posted by K Sengupta on 2008-04-04 06:10:01

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