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A046820
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Number of 1's in binary expansion of 5n.
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2
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0, 2, 2, 4, 2, 3, 4, 3, 2, 4, 3, 5, 4, 2, 3, 4, 2, 4, 4, 6, 3, 4, 5, 5, 4, 6, 2, 4, 3, 3, 4, 5, 2, 4, 4, 6, 4, 5, 6, 4, 3, 5, 4, 6, 5, 4, 5, 6, 4, 6, 6, 8, 2, 3, 4, 4, 3, 5, 3, 5, 4, 4, 5, 6, 2, 4, 4, 6, 4, 5, 6, 5, 4, 6, 5, 7, 6, 3, 4, 5, 3, 5, 5, 7, 4, 5, 6, 6, 5, 7, 4, 6, 5
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OFFSET
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0,2
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COMMENTS
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a(n) is also the largest integer such that 2^a(n) divides binomial(10n, 5n). - Benoit Cloitre, Mar 27 2002
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LINKS
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FORMULA
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a(n) = floor(log(gcd(binomial(10*n, 5*n), 2^floor(log(binomial(10*n, 5*n))/log(2))))/log(2)). - Benoit Cloitre, Mar 27 2002
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EXAMPLE
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For n = 10, 5*n = 50 = 110010_2, having 3 1's. So, a(10) = 3. - Indranil Ghosh, Jan 18 2017
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MATHEMATICA
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a[n_] := DigitCount[5*n, 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 18 2023 *)
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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