A004218 a(n) = log_10(n) rounded up.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is the number of terms in the sequence A011557 (Powers of 10) that are less than n. For n > 1, a(n) is the number of digits in n-1. - Tanya Khovanova, Jun 22 2007

Examples

			From _M. F. Hasler_, Dec 07 2018: (Start)
log_10(1) = 0, therefore a(1) = 0.
log_10(2) = 0.301..., therefore a(2) = 1.
log_10(9) = 0.954..., therefore a(9) = 1.
log_10(10) = 1, therefore a(10) = 1.
log_10(11) = 1.04..., therefore a(11) = 2.
log_10(99) = 1.9956..., therefore a(99) = 2.
log_10(100) = 2, therefore a(100) = 2.
log_10(101) = 2.004..., therefore a(101) = 3. (End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004216, A007953, A055642.

Programs

Haskell

a004218 n = if n == 1 then 0 else 1 + a004216 (n - 1)

Maple

A004218 := proc(n)
    ceil(log[10](n)) ;
end proc:
seq(A004218(n),n=1..120) ; # R. J. Mathar, May 16 2023

Mathematica

Array[Ceiling[Log10[#]] &, 100] (* Amiram Eldar, Dec 08 2018 *)

PARI

A004218(n)=logint(n-(n>1),10)+1 \\ M. F. Hasler, Dec 07 2018

Formula

a(1) = 0, a(n) = 1 + A004216(n-1) for n > 1. - Reinhard Zumkeller, Dec 22 2012

a(n) = A055642(n-1) for all n > 1. a(n+1) is the number of decimal digits of n if 0 is considered to have 0 digits. - M. F. Hasler, Dec 07 2018