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I’m interested in some sequences which have no square factor. $$ s_i =\begin{cases} 4 & i=0; \\\\ s_{i-1}^2 - 2 & \text{otherwise} \end{cases}$$ This is Lucas–Lehmer primality test sequence. A003010 in OEIS.

when ${s_i}$ has a square factor? I had checked that the sequence has no square factor for i=1,2,...,7

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    I edited this by using MythType. I don't know why Tex doesn't work here. Could you help me? what's "TeX ed"2010-08-27
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    @a-boy: I was saying that you have "Texed" the question properly. Thats all!2010-08-27

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