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A204988
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The index j < k such that n divides 2^k - 2^j, where k is the least index (A204987) for which such j exists.
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3
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1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1
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OFFSET
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1,4
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COMMENTS
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For a guide to related sequences, see A204892.
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LINKS
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FORMULA
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The above conjecture is true because the definition of this sequence and A204987 requires j to be at least 1 and 2^k - 2^j can be written 2^j*(2^(k-j) - 1).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/2. - Amiram Eldar, Oct 22 2022
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EXAMPLE
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MATHEMATICA
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a[n_] := Max[1, IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Oct 22 2022 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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