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**tommy20****Guest**

We have sequence, wich is define by the conditions:

Decide if exist any integer number

and**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 693
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It is clear that none of the terms in the sequence is divisible by 5. For

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Similarly none of the terms is divisible by 3, for

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It follows that

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i.e. consecutive terms are coprime; also

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i.e. alternate terms are coprime as well.

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Since *a*₁ = 1, *k* =1 fits the bill. And since the sequence is clearly strictly increasing, it is the only one that does.

Me, or the ugly man, whatever (3,3,6)

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