[list=*]

[*]

[/list]

Similarly none of the terms is divisible by 3, for

[list=*]

[*]

[/list]

It follows that

[list=*]

[*]

[/list]

i.e. consecutive terms are coprime; also

[list=*]

[*]

[/list]

i.e. alternate terms are coprime as well.

[list=*]

[*]

[/list]

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

Decide if exist any integer number

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