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
KEYWORD
nonn
AUTHOR
STATUS
approved
