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Final nonzero digit of n! in base 12.
16

%I #30 Jan 08 2023 14:20:19

%S 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,

%T 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,

%U 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

%N Final nonzero digit of n! in base 12.

%C 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

%H Michael De Vlieger, <a href="/A136698/b136698.txt">Table of n, a(n) for n = 0..10368</a> (10368 = 6 * 12^3)

%H Jean-Marc Deshouillers, <a href="https://web.archive.org/web/20171109074916/https://math.boku.ac.at/udt/vol07/no1/03Desh30-11.pdf">A footnote to the least non zero digit of n! in base 12</a>, Uniform Distribution Theory 7:1 (2012), pp. 71-73. [Wayback Machine link]

%H Jean-Marc Deshouillers, <a href="https://doi.org/10.1515/udt-2016-0018">Yet Another Footnote to the Least Non Zero Digit of n! in Base 12</a>. Unif. Distrib. Theory 11 (2016), no. 2, 163-167.

%H Jean-Marc Deshouillers and Imre Ruzsa, <a href="http://doi.org/10.5486/PMD.2011.5169">The least nonzero digit of n! in base 12</a>, Publicationes Mathematicae, Vol. 79, No. 3-4 (2011), pp. 395-400.

%H Jean-Marc Deshouillers, Laurent Habsieger, Shanta Laishram, and Bernard Landreau, <a href="https://arxiv.org/abs/1611.08180">Sums of the digits in bases 2 and 3</a>, arXiv:1611.08180 [math.NT], 2016. (See first page footnote.)

%e 6! = 720 decimal = 500 duodecimal, so a(6) = 5.

%t a136698[n_Integer] := Last[Select[IntegerDigits[n!, 12], # > 0 &]]; a136698 /@ Range[0, 144] (* _Michael De Vlieger_, Aug 13 2014 *)

%Y Cf. A000142, A136690, A136691, A136692, A136693, A136694, A136695, A136696, A008904, A136697, A136699, A136700, A136701, A136702.

%K base,easy,nonn

%O 0,3

%A _Carl R. White_, Jan 16 2008