A279766 Number of odd digits in the decimal expansions of integers 1 to n.

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 60, 61, 61, 62, 62, 63, 63, 64, 64

Offset: 0

Author

Joseph Myers, Dec 18 2016

Keywords

• base
• nonn

Comments

From Bernard Schott, Feb 19 2023: (Start)

Problem 1 of the British Mathematical Olympiad, round 1, in 2016/2017 asked: when the integers 1, 2, 3, ..., 2016 are written down in base 10, how many of the digits in the list are odd? The answer is a(2016) = 4015.

The similar sequence but with number of even digits is A358854. (End)

Links

• Joseph Myers, Table of n, a(n) for n = 0..1000
• United Kingdom Mathematics Trust, 2016/17 British Mathematical Olympiad Round 1, Problem 1.
• Index to sequences related to Olympiads.

Crossrefs

Cf. A007908, A058183, A117804, A196564, A358854.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+
      nops(select(x-> x::odd, convert(n,base,10))))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 22 2016

Mathematica

Table[Count[Flatten@ IntegerDigits@ Range[0, n], d_ /; OddQ@ d], {n, 0, 68}] (* or *)
Accumulate@ Table[Count[IntegerDigits@ n, d_ /; OddQ@ d], {n, 0, 68}] (* Michael De Vlieger, Dec 22 2016 *)

Formula

a(n) = A196564(A007908(n)). - Michel Marcus, Dec 18 2016

a(n) = A117804(n+1) - A358854(n) (number of total digits - number of even digits). - Bernard Schott, Feb 19 2023