login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A279766
Number of odd digits in the decimal expansions of integers 1 to n.
3
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
0,4
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)
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
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 *)
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Joseph Myers, Dec 18 2016
STATUS
approved