cp's OEIS Frontend

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

%I A241730 #16 Apr 29 2014 06:06:43
%S A241730 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,
%T A241730 28,29,31,32,34,35,37,39,40,42,43,45,46,48,50,51,53,55,56,58,60,61,63,
%U A241730 65,66,68,70,72,73,75,77,79,80,82,84,86,88,89,91,93,95,97,99,100,102,104,106
%N A241730 Number of digits in the decimal expansion of n! minus the number of digits in the decimal expansion of n.
%H A241730 Charles R Greathouse IV, <a href="/A241730/b241730.txt">Table of n, a(n) for n = 0..10000</a>
%F A241730 a(n) = floor(log(n!)/log(10)) - floor(log(n)/log(10)) for n > 0.
%F A241730 a(n) = A034886(n) - A055642(n).
%e A241730 a(5) = 2 because 5! = 120 has three digits, 5 has only one digit, and 3 - 1 = 2.
%e A241730 a(6) = 2 because 6! = 720 has three digits, 6 has only one digit, and 3 - 1 = 2.
%e A241730 a(7) = 3 because 7! = 5040 has four digits, 7 has only one digit, and 4 - 1 = 3.
%p A241730 seq(nops(convert(n!,base,10)) - nops(convert(n,base,10)), n=0..50); # _Peter Luschny_, Apr 28 2014
%t A241730 Table[Length[IntegerDigits[n!]] - Length[IntegerDigits[n]], {n, 0, 79}]
%o A241730 (PARI) a(n)=lngamma(n+1)\log(10)-#Str(n)+1 \\ _Charles R Greathouse IV_, Apr 28 2014
%Y A241730 Cf. A034886, A101506.
%K A241730 nonn,easy,base
%O A241730 0,6
%A A241730 _Alonso del Arte_, Apr 27 2014