A243293 Number of factorials < 10^n.

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, 25, 26, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 44, 45, 46, 46, 47, 47, 48, 49, 49, 50, 50, 51, 52, 52, 53, 53

Offset

1,1

Comments

A181590(150) = 95 does not agree with a(150) = 96.

0! and 1! are the same number so a(n) counts it as 1 number.

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

There are 4 factorials < 10^2: 0! = 1! = 1, 2! = 2, 3! = 6, and 4! = 24. Thus a(2) = 4.

Mathematica

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 *)

Prog

(PARI) a(n) = {my(tot=0); for(k=1, 10^n, if(k!<10^n, tot++); if(k!>=10^n, break)); return(tot)}
n=1; while(n<100, print1(a(n), ", "); n++)

Crossrefs

Cf. A000142, A181590.

Sequence in context: A260158 A317093 A181590 * A078923 A165240 A350398

Adjacent sequences: A243290 A243291 A243292 * A243294 A243295 A243296

Keyword

nonn

Author

Derek Orr, Jun 02 2014

Status

approved