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

0,6

Links

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

Formula

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

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

Example

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.

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}]

Prog

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

Crossrefs

Cf. A034886, A101506.

Sequence in context: A182220 A127037 A089646 * A011884 A029070 A344672

Adjacent sequences: A241727 A241728 A241729 * A241731 A241732 A241733

Keyword

nonn,easy,base

Author

Alonso del Arte, Apr 27 2014

Status

approved