A090105 Decimal value of largest digit of n! when it was written in base n.

1, 1, 2, 2, 4, 3, 6, 6, 7, 8, 10, 5, 12, 6, 12, 8, 16, 14, 18, 19, 20, 20, 22, 23, 23, 24, 25, 24, 28, 29, 30, 29, 31, 30, 32, 33, 36, 37, 33, 39, 40, 40, 42, 40, 43, 45, 46, 45, 46, 47, 49, 51, 52, 51, 54, 55, 56, 56, 58, 59, 60, 60, 61, 63, 62, 64, 66, 67, 68, 65, 70, 67, 72, 71

Offset: 1

Author

Labos Elemer, Dec 17 2003

Keywords

• base
• nonn

Examples

			For n=12: 12! = 114500000_12, so a(12) = 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006993, A090104, A216377.

Programs

Maple

f:= n -> max(convert(n!,base,n)): f(1):= 1:map(f, [$1..100]); # Robert Israel, Dec 09 2020

Mathematica

Table[Max[IntegerDigits[w!, w]], {w, 2, 100}]

PARI

a(n) = if(n==1, 1, vecmax(digits(n!, n))) \\ Felix Fröhlich, Dec 09 2020