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A136698
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Final nonzero digit of n! in base 12.
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16
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1, 1, 2, 6, 2, 10, 5, 11, 4, 6, 7, 5, 5, 5, 10, 6, 8, 4, 11, 5, 4, 7, 10, 2, 4, 4, 8, 6, 6, 6, 3, 9, 8, 10, 4, 8, 11, 11, 10, 6, 4, 8, 10, 10, 8, 6, 1, 11, 8, 8, 4, 2, 8, 4, 9, 3, 10, 6, 1, 11, 7, 7, 2, 6, 8, 4, 4, 4, 8, 4, 4, 8, 4, 4, 8, 2, 8, 4, 8, 8, 4, 3, 6, 6, 6, 6, 7, 9, 2, 10, 3, 9, 5, 9, 6, 6, 8, 8, 4
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OFFSET
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0,3
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COMMENTS
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The asymptotic densities of the numbers k such that a(k) = m is 1/2 for m = 4 or 8, and 0 otherwise (Deshouillers and Ruzsa, 2011). Therefore, the asymptotic mean of this sequence is 6. There are infinitely many numbers k such that a(k) = m for each of the values m = 3, 6, or 9 (Deshouillers, 2012). - Amiram Eldar, Jan 11 2021
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LINKS
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Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram, and Bernard Landreau, Sums of the digits in bases 2 and 3, arXiv:1611.08180 [math.NT], 2016. (See first page footnote.)
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EXAMPLE
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6! = 720 decimal = 500 duodecimal, so a(6) = 5.
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MATHEMATICA
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a136698[n_Integer] := Last[Select[IntegerDigits[n!, 12], # > 0 &]]; a136698 /@ Range[0, 144] (* Michael De Vlieger, Aug 13 2014 *)
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CROSSREFS
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Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136699, A136700, A136701, A136702.
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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