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A004218
a(n) = log_10(n) rounded up.
10
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
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
STATUS
approved