A137233 Number of n-digit even numbers.

5, 45, 450, 4500, 45000, 450000, 4500000, 45000000, 450000000, 4500000000, 45000000000, 450000000000, 4500000000000, 45000000000000, 450000000000000, 4500000000000000, 45000000000000000, 450000000000000000

Offset

1,1

Comments

From Kival Ngaokrajang, Oct 18 2013: (Start)

a(n) is also the total number of double rows identified numbers in n digit.

For example:

n = 1: 01 23 45 67 89 = 5 double rows;

n = 2: 1011 1213 1415 1617 1819...9899 = 45 double rows;

n = 3: 100101 102103 104105...998999 = 450 double rows;

...

The number of double rows is also A030656. (End)

a(n) is also the number of n-digit integers with an even number of even digits (A356929); a(5) = 45000 is the answer to the question 2 of the Olympiade Mathématique Belge in 2004 (link). - Bernard Schott, Sep 06 2022

a(n) is also the number of n-digit integers with an odd number of odd digits (A054684). - Bernard Schott, Nov 07 2022

Links

Table of n, a(n) for n=1..18.

Olympiade Mathématique Belge, OMB 2004, Finale Maxi, Question 2.

Index to sequences related to Olympiads.

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

a(n) = 9*10^(n-1)/2 if n > 1. - R. J. Mathar, May 23 2008

Example

a(2) = 45 because there are 45 2-digit even numbers.

Prog

(Python)
def A137233(n): return 9*10**(n-1)+1>>1 # Chai Wah Wu, Nov 11 2022

Crossrefs

Cf. A002275, A090843, A097166, A099914, A099915, A037487, A000422, A057138, A014925, A014923, A016313, A002276, A011577, A019518, A053052.

Cf. A054684, A356929.

Sequence in context: A346580 A054318 A093140 * A357205 A001449 A371756

Adjacent sequences: A137230 A137231 A137232 * A137234 A137235 A137236

Keyword

easy,nonn,base

Author

Ctibor O. Zizka, Mar 08 2008

Extensions

Corrected and extended by R. J. Mathar, May 23 2008

Status

approved