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Algorithm to generate an increasing sequence of integers

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Design an algorithm to generate the sequence of positive integers (in increasing order) whose only prime divisors are 2 and 3; that is, your program should produce the sequence 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, ... . Does your program represent an algorithm in the strict sense?

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Solution Summary

A SQL algorithm to generate the increasing sequence of positive integers whose only prime divisors are 2 and 3. The version will run in SQL 2008 or any edition that supports the += operator. The algorithm can serve as a basis to other SQL languages and implementations or work as pseudo-coded in other contexts.

Comment is made on whether this solution can be considered an algorithm in the strict sense.

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A strict algorithm must stop in a finite time. Since "the sequence of positive integers..." has no end (it is infinite), no algorithm in the strict sense can produce it. We could head in the direction of something producible by a strict algorithm by changing the requirement to something like "the sequence of positive integers less than or equal to 200..."

How do we know that the given sequence is infinite? Let us assume, it is not. Then, there is a greatest number ...

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