A136698 Final nonzero digit of n! in base 12.
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
Examples
6! = 720 decimal = 500 duodecimal, so a(6) = 5.
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.
Crossrefs
Programs
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Mathematica
a136698[n_Integer] := Last[Select[IntegerDigits[n!, 12], # > 0 &]]; a136698 /@ Range[0, 144] (* Michael De Vlieger, Aug 13 2014 *)
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PARI
a(n) = my(d=digits(n!, 12)); forstep(k=#d, 1, -1, if (d[k], return(d[k]))); \\ Michel Marcus, Feb 18 2025
Comments