# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a243293 Showing 1-1 of 1 %I A243293 #19 Feb 22 2020 22:14:07 %S A243293 3,4,6,7,8,9,10,11,12,13,14,14,15,16,17,18,18,19,20,21,21,22,23,24,24, %T A243293 25,26,26,27,28,29,29,30,31,31,32,33,33,34,34,35,36,36,37,38,38,39,40, %U A243293 40,41,41,42,43,43,44,44,45,46,46,47,47,48,49,49,50,50,51,52,52,53,53 %N A243293 Number of factorials < 10^n. %C A243293 A181590(150) = 95 does not agree with a(150) = 96. %C A243293 0! and 1! are the same number so a(n) counts it as 1 number. %C A243293 a(n) is also the number of terms needed in the series Sum_{k=0..m} 1/k! to calculate exp(1) with a precision of at least n - 1 digits, i.e., exp(1) - Sum_{k=0..a(n)}1/k! < 10^(-n). - _Martin Renner_, Feb 18 2020 %H A243293 Giovanni Resta, Table of n, a(n) for n = 1..10000 %e A243293 There are 4 factorials < 10^2: 0! = 1! = 1, 2! = 2, 3! = 6, and 4! = 24. Thus a(2) = 4. %t A243293 f=1; t=0; n=10; L={}; While[Length[L] < 100, t++; f*=t; While[f > n, AppendTo[ L, t-1]; n *= 10]]; L (* _Giovanni Resta_, Feb 19 2020 *) %o A243293 (PARI) a(n) = {my(tot=0); for(k=1,10^n,if(k!<10^n,tot++); if(k!>=10^n, break)); return(tot)} %o A243293 n=1; while(n<100,print1(a(n),", "); n++) %Y A243293 Cf. A000142, A181590. %K A243293 nonn %O A243293 1,1 %A A243293 _Derek Orr_, Jun 02 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE