OFFSET
0,6
COMMENTS
The total number of digits >= 4 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012
LINKS
Hieronymus Fischer, Table of n, a(n) for n = 0..10000
FORMULA
From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 3/5)*(2n + 2 + (1/5 - floor(n/10^j + 3/5))*10^j) - floor(n/10^j)*(2n + 2 - (1 + floor(n/10^j)) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A102673(n) + (1/2)*Sum_{j=1..m+1} (((1/5)*floor(n/10^j + 3/5) + floor(n/10^j))*10^j - (floor(n/10^j + 3/5)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m - 1) = 6*m*10^(m-1).
(This is the total number of digits >= 4 occurring in all the numbers with <= m places.)
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(4*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)
MAPLE
p:=proc(n) local b, ct, j: b:=convert(n, base, 10): ct:=0: for j from 1 to nops(b) do if b[j]>=4 then ct:=ct+1 else ct:=ct fi od: ct: end:seq(add(p(i), i=0..n), n=0..90); # Emeric Deutsch, Feb 22 2005
MATHEMATICA
Accumulate[Table[Total[Drop[Most[DigitCount[n]], 3]], {n, 0, 80}]] (* Harvey P. Dale, Nov 27 2015 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 03 2005
EXTENSIONS
More terms from Emeric Deutsch, Feb 22 2005
STATUS
approved