A057717 The non-powers of 10.

0, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

0,2

Comments

a(n) is the length signature of a string plus its length.

Links

Table of n, a(n) for n=0..68.

Formula

a(n) = ceiling(log_10(a(n) + 1)) + n.

Find k such that 10^k - (k + 1) <= n < 10^(k+1) - (k + 2), then a(n) = n + k + 1.

Mathematica

With[{upto=100}, Complement[Range[0, upto], 10^Range[0, Floor[Log10[ upto]]]]] (* Harvey P. Dale, Nov 01 2016 *)

Prog

(Python)
def A057717(n): return n+(m:=len(str(n-1)))+(n>=10**m-m) if n else 0 # Chai Wah Wu, Jun 30 2024
(Python)
from itertools import count, islice
def agen(): # generator of terms
    yield 0
    yield from (j for i in count(0) for j in range(10**i+1, 10**(i+1)))
print(list(islice(agen(), 70))) # Michael S. Branicky, Oct 11 2024

Crossrefs

Complement of A011557. Cf. A057716.

Sequence in context: A364274 A118764 A226134 * A183222 A063742 A014089

Adjacent sequences: A057714 A057715 A057716 * A057718 A057719 A057720

Keyword

nonn

Author

John Lindgren (john.lindgren(AT)Eng.Sun.COM), Oct 24 2000

Extensions

Better description from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 29 2001

Status

approved