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 A094798 Number of times 1 is used in writing out all the numbers 1 through n. 6

%I

%S 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,

%T 13,13,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,16,

%U 16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18

%N Number of times 1 is used in writing out all the numbers 1 through n.

%C 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

%C A014778 gives the fixed points. - _David Wasserman_, Feb 22 2005

%C Partial sums of A268643. - _Robert Israel_, Oct 28 2016

%H Harvey P. Dale, <a href="/A094798/b094798.txt">Table of n, a(n) for n = 1..1000</a>

%F 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

%p 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

%p ListTools:-PartialSums([seq(numboccur(1,convert(n,base,10)),n=1..100)]); # _Robert Israel_, Oct 28 2016

%t Accumulate[Table[DigitCount[n,10,1],{n,80}]] (* _Harvey P. Dale_, Sep 27 2013 *)

%Y Cf. A014778, A053541.

%K easy,base,nonn

%O 1,10

%A _Lekraj Beedassy_, Jun 11 2004

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Last modified July 15 16:58 EDT 2019. Contains 325051 sequences. (Running on oeis4.)