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A358684
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a(n) is the minimum integer k such that the smallest prime factor of the n-th Fermat number exceeds 2^(2^n - k).
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0
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0, 0, 0, 0, 0, 23, 46, 73, 206, 491, 999, 2030, 4080, 8151
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OFFSET
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0,6
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COMMENTS
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Conjecture: the dyadic valuation of A093179(n) - 1 does not exceed 2^n - a(n).
a(14) is probably equal to 16208; a(15) to a(19) are 32738, 65507, 131028, 262121, 524252; a(20) is unknown; a(21) to a(23) are 2097110, 4194189, 8388581; a(24) is unknown.
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LINKS
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FORMULA
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Conjecture: a(n) ~ 2^n as n -> oo.
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EXAMPLE
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For n=5, the smallest prime factor of F(5) = 2^(2^5) + 1 is 641 and it falls between 2^(2^5 - 23) = 512 < 641 < 1024 = 2^(2^5 - 22) so that a(5) = 23.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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