The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A102674

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A102674

Number of digits >= 4 in the decimal representations of all integers from 0 to n.
(history; published version)

#23 by Michael De Vlieger at Wed Nov 16 17:26:57 EST 2022

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proposed

approved

#22 by Michel Marcus at Wed Nov 16 16:35:56 EST 2022

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editing

proposed

#21 by Michel Marcus at Wed Nov 16 16:35:53 EST 2022

FORMULA

Contribution from _From _Hieronymus Fischer_, Jun 10 2012 : (Start):

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approved

editing

#20 by N. J. A. Sloane at Thu Aug 17 22:29:13 EDT 2017

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proposed

approved

#19 by Jon E. Schoenfield at Thu Aug 17 21:18:49 EDT 2017

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editing

proposed

#18 by Jon E. Schoenfield at Thu Aug 17 21:18:43 EDT 2017

FORMULA

a(n) = (1/2)*sum_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_Sum_{j=1..m+1} ((0.2(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 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_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

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approved

editing

#17 by Harvey P. Dale at Fri Nov 27 12:00:51 EST 2015

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editing

approved

#16 by Harvey P. Dale at Fri Nov 27 12:00:45 EST 2015

MATHEMATICA

Accumulate[Table[Total[Drop[Most[DigitCount[n]], 3]], {n, 0, 80}]] (* Harvey P. Dale, Nov 27 2015 *)

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approved

editing

#15 by N. J. A. Sloane at Mon Nov 04 21:48:19 EST 2013

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proposed

approved

#14 by Jon E. Schoenfield at Mon Nov 04 21:05:51 EST 2013

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editing

proposed