login
A094798
Number of times 1 is used in writing out all the numbers 1 through n.
9
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18
OFFSET
1,10
COMMENTS
The number of 1's required to write all integers of n or fewer digits (i.e., the sequence a(9), a(99), a(999), ...) is 1, 20, 300, 4000, ..., which is A053541. - Jason D. W. Taff (jtaff(AT)jburroughs.org), Dec 05 2004
A014778 gives the fixed points. - David Wasserman, Feb 22 2005
Partial sums of A268643. - Robert Israel, Oct 28 2016
LINKS
FORMULA
G.f. g(x) satisfies g(x) = x/((1-x)*(1-x^10)) + ((1-x^10)/(1-x))^2*g(x^10). - Robert Israel, Oct 28 2016 [corrected by Fabio VisonĂ , Aug 10 2022]
MAPLE
nones:=proc(n) local nn, c, j: nn:=convert(n, base, 10): c:=0: for j to nops(nn) do if nn[j]=1 then c:=c+1 else end if end do: c end proc: a:=proc(n) options operator, arrow: add(nones(k), k=1..n) end proc: seq(a(n), n=1..75); # Emeric Deutsch, Mar 01 2008
ListTools:-PartialSums([seq(numboccur(1, convert(n, base, 10)), n=1..100)]); # Robert Israel, Oct 28 2016
MATHEMATICA
Accumulate[Table[DigitCount[n, 10, 1], {n, 80}]] (* Harvey P. Dale, Sep 27 2013 *)
PROG
(Python)
from itertools import accumulate, count, islice
def f(_, n): return _ + str(n).count("1")
def agen(): yield from accumulate(count(1), f)
print(list(islice(agen(), 75))) # Michael S. Branicky, Aug 09 2022
(PARI) a(n) = sum(k=1, n, #select(x->(x==1), digits(k))); \\ Michel Marcus, Oct 03 2023
CROSSREFS
KEYWORD
easy,base,nonn
AUTHOR
Lekraj Beedassy, Jun 11 2004
STATUS
approved