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oeis_358684_conjecture_0

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Conjecture: the dyadic valuation of A93179(n) - 1 does not exceed 2^n - a(n). A93179(n) is minFac(fermatNumber n), the smallest prime factor of the n-th Fermat number. The conjecture states that if $P_n$ is the smallest prime factor of the $n$-th Fermat number, then $\nu_2(P_n - 1) \le 2^n - a(n)$. Substituting the definition of $a(n)$, this is equivalent to $\nu_2(P_n - 1) \le \lfloor \log_2(P_n) \rfloor$. This is Conjecture 3.4 in [SA22].

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Lean 4 Statement
theorem oeis_358684_conjecture_0 (n : ℕ) :
    padicValNat 2 (minFac (fermatNumber n) - 1) ≤ 2 ^ n - a n
ID: OEIS__358684__oeis_358684_conjecture_0
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