A241730 Number of digits in the decimal expansion of n! minus the number of digits in the decimal expansion of n.

0, 0, 0, 0, 1, 2, 2, 3, 4, 5, 5, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106

Offset: 0

Author

Alonso del Arte, Apr 27 2014

Keywords

• nonn
• easy
• base

Examples

			a(5) = 2 because 5! = 120 has three digits, 5 has only one digit, and 3 - 1 = 2.
a(6) = 2 because 6! = 720 has three digits, 6 has only one digit, and 3 - 1 = 2.
a(7) = 3 because 7! = 5040 has four digits, 7 has only one digit, and 4 - 1 = 3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A034886, A101506.

Programs

Maple

seq(nops(convert(n!,base,10)) - nops(convert(n,base,10)), n=0..50); # Peter Luschny, Apr 28 2014

Mathematica

Table[Length[IntegerDigits[n!]] - Length[IntegerDigits[n]], {n, 0, 79}]

PARI

a(n)=lngamma(n+1)\log(10)-#Str(n)+1 \\ Charles R Greathouse IV, Apr 28 2014

Formula

a(n) = floor(log(n!)/log(10)) - floor(log(n)/log(10)) for n > 0.

a(n) = A034886(n) - A055642(n).