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Xavier writes down a sequence of positive integers on a blackboard, beginning with 1. Each term thereafter equals the smallest positive integer which cannot be expressed as the product of one or more distinct terms already on the blackboard. The first several terms of Xavier’s sequence are 1, 2, 3, 4, 5, 7, and 9. He stops writing when he first writes a number greater than 1000. At this point, how many composite numbers will Xavier have written?

 Jan 6, 2019
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1, 2, 3, 4, 5, 7,  9, 11, 13, 17, 19, 23......only prime numbers can be written from here on to 1009, which is a prime number.
So, you only have: 4, 9 the only two composite numbers that you can write between 1 and 1009.

 Jan 6, 2019

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