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A136698
Final nonzero digit of n! in base 12.
16
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
OFFSET
0,3
COMMENTS
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
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10368 (10368 = 6 * 12^3)
Jean-Marc Deshouillers, A footnote to the least non zero digit of n! in base 12, Uniform Distribution Theory 7:1 (2012), pp. 71-73. [Wayback Machine link]
Jean-Marc Deshouillers, Yet Another Footnote to the Least Non Zero Digit of n! in Base 12. Unif. Distrib. Theory 11 (2016), no. 2, 163-167.
Jean-Marc Deshouillers and Imre Ruzsa, The least nonzero digit of n! in base 12, Publicationes Mathematicae, Vol. 79, No. 3-4 (2011), pp. 395-400.
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.)
Jean-Marc Deshouillers, Pascal Jelinek, and Lukas Spiegelhofer, Binary-ternary collisions and the last significant digit of n! in base 12, arXiv:2412.09124 [math.NT], 2024.
EXAMPLE
6! = 720 decimal = 500 duodecimal, so a(6) = 5.
MATHEMATICA
a136698[n_Integer] := Last[Select[IntegerDigits[n!, 12], # > 0 &]]; a136698 /@ Range[0, 144] (* Michael De Vlieger, Aug 13 2014 *)
KEYWORD
base,easy,nonn,changed
AUTHOR
Carl R. White, Jan 16 2008
STATUS
approved