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

Author

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

Keywords

• nonn

Comments

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

Crossrefs

Complement of A011557. Cf. A057716.

Programs

Mathematica

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

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

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.

Extensions

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