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”).

A358854
Number of even digits necessary to write all the numbers from 0 up to n.
3
1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 66, 66, 67, 67, 68, 68
OFFSET
0,3
COMMENTS
Inspired by problem 1 of British Mathematical Olympiad, round 1, in 2016/2017 (link).
FORMULA
a(n) = A117804(n+1) - A279766(n) (number of total digits - number of odd digits).
a(n) = Sum_{k=0..n} A196563(k).
MAPLE
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+
nops(select(x-> x::even, convert(n, base, 10))))
end:
seq(a(n), n=0..100); # Alois P. Heinz, Feb 19 2023
MATHEMATICA
Accumulate[Table[Count[IntegerDigits[n], _?EvenQ], {n, 0, 100}]] (* Amiram Eldar, Dec 03 2022 *)
PROG
(Python)
from itertools import accumulate, count, islice
def A196563(n): return sum(1 for d in str(n) if d in "02468")
def agen(): yield from accumulate(A196563(n) for n in count(0))
print(list(islice(agen(), 76))) # Michael S. Branicky, Dec 03 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Dec 03 2022
STATUS
approved