

A004218


log_10(n) rounded up.


8



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
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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 n1.  Tanya Khovanova, Jun 22 2007


LINKS

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


FORMULA

a(n) = if n == 1 then 0 else 1 + A004216(n1).  Reinhard Zumkeller, Dec 22 2012
a(n) = A055642(n1) 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)


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: A231560 A113679 A262438 * A044931 A178487 A280560
Adjacent sequences: A004215 A004216 A004217 * A004219 A004220 A004221


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



