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A202709
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(Sum of digits of n!!) / 9.
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0
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2, 2, 2, 2, 2, 2, 4, 5, 5, 4, 5, 5, 4, 6, 7, 5, 8, 5, 8, 8, 10, 10, 10, 9, 12, 9, 12, 9, 14, 10, 12, 12, 16, 9, 16, 10, 15, 13, 16, 14, 17, 12, 20, 15, 20, 15, 19, 20, 20, 19, 22, 20, 22, 18, 21, 21, 24, 25, 27, 19, 27, 23, 26, 23, 28, 27, 25, 23, 27, 23, 29, 31
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OFFSET
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11,1
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COMMENTS
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(sum of digits of n!!) / 9 is an integer for n = 9 and n > 10.
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LINKS
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FORMULA
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a(n) << n log n. Presumably a(n) ~ n log n but proving this requires showing that not too many digits are 0. (The trailing 0's in even terms are not a problem, being only about n/8.) The expected constant is 1 / (4 log 10) = 0.10857.... [Charles R Greathouse IV, Dec 23 2011]
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MATHEMATICA
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Table[Sum[DigitCount[n!!][[i]]*i/9, {i, 1, 9}], {n, 11, 100}]
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PROG
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(PARI) a(n)=my(v=eval(Vec(Str(prod(k=1, n\2, 2*k+n%2))))); sum(i=1, #v, v[i])/9 \\ Charles R Greathouse IV, Dec 23 2011
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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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EXTENSIONS
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a(37), a(41), a(45), a(46) corrected by Georg Fischer, Jul 15 2024
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STATUS
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approved
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