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A102674 Number of digits >= 4 in the decimal representations of all integers from 0 to n. 2
0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 10, 11, 12, 12, 12, 12, 12, 13, 14, 15, 16, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 36, 38, 40, 41, 42, 43, 44, 46, 48, 50, 52, 54, 56, 57, 58, 59, 60, 62, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78 (list; graph; refs; listen; history; text; internal format)
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
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
Partial sums of A102673.
Cf. A000120, A000788, A023416, A059015 (for base 2).
Sequence in context: A101272 A006160 A071640 * A097623 A198462 A069754
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 03 2005
EXTENSIONS
More terms from Emeric Deutsch, Feb 22 2005
STATUS
approved

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Last modified February 20 20:29 EST 2024. Contains 370217 sequences. (Running on oeis4.)