A001637 Numbers with an even number of digits.

10, 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, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 1000, 1001

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. A001633 (complement), A055642.

Programs

Haskell

a001637 n = a001637_list !! (n-1)
a001637_list = filter (even . a055642) [0..]
-- Reinhard Zumkeller, Jul 14 2014

Mathematica

Select[Range[0, 1001], EvenQ[Length[IntegerDigits[#]]] &] (* T. D. Noe, Aug 09 2012 *)

PARI

is(n)=#Str(n)%2==0 \\ Charles R Greathouse IV, Nov 26 2018

PARI

a(n) = n + 100^logint(110*n,100) \ 11; \\ Kevin Ryde, Nov 10 2022

Python

def a(n): return n + (100**((len(str(110*n))-1)//2) - 1)//11
print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Nov 10 2022 after Kevin Ryde

Formula

A055642(a(n)) mod 2 = 0. - Reinhard Zumkeller, Jul 14 2014

a(n) = n + (100^floor(log_100(110*n)) - 1)/11. - Kevin Ryde, Nov 10 2022