Simple recurrence that fails to be integer for the first time at the 44th term – mathoverflow.net

Simple recurrence that fails to be integer for the first time at the 44th term – mathoverflow.net

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The sequence defined by $a_0=a_1 =1$ and $$ a_n = \frac{1}{n-1}\sum_{i=0}^{n-1}a_i^2, \quad n > 1 $$ fails to be integer for the first time at $a_{44}$. Why?? You can verify the statement by ...

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