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

1,11

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

Links

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

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

Example

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)

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 *)

Prog

(Haskell) a004218 n = if n == 1 then 0 else 1 + a004216 (n - 1)
(PARI) A004218(n)=logint(n-(n>1), 10)+1 \\ M. F. Hasler, Dec 07 2018

Crossrefs

Cf. A004216, A007953, A055642.

Sequence in context: A211665 A239374 A262190 * A055642 A348674 A276502

Adjacent sequences: A004215 A004216 A004217 * A004219 A004220 A004221

Keyword

nonn

Author

N. J. A. Sloane

Status

approved