A001633 Numbers with an odd number of digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

The lower and upper asymptotic densities of this sequence are 1/11 and 10/11, respectively. - Amiram Eldar, Feb 01 2021

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001637 (complement), A055642.

Programs

Haskell

a001633 n = a001633_list !! (n-1)
a001633_list = filter (odd . a055642) [0..]
-- Reinhard Zumkeller, Jul 14 2014

Mathematica

Select[Range[0, 145], OddQ[Length[IntegerDigits[#]]] &] (* T. D. Noe, Aug 09 2012 *)
Table[Range[10^n,10^(n+1)-1],{n,0,4,2}]//Flatten (* Harvey P. Dale, Nov 29 2022 *)

PARI

is(n)=#Str(n)%2 \\ Charles R Greathouse IV, Nov 26 2018

Scala

(0 to 199).filter(Integer.toString().length % 2 == 1) // _Alonso del Arte, Feb 03 2020

Formula

A055642(a(n)) mod 2 = 1. - Reinhard Zumkeller, Jul 14 2014

Except for k = 0, if k is in this sequence, floor(log_10 k) is even; e.g., if k has three digits, 2 <= log_10 k < 3. - Alonso del Arte, Feb 03 2020