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#20 by Michael De Vlieger at Wed Nov 16 17:26:39 EST 2022
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#19 by Michel Marcus at Wed Nov 16 16:38:00 EST 2022
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#18 by Michel Marcus at Wed Nov 16 16:37:57 EST 2022
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| FORMULA
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Contribution fromFrom Hieronymus Fischer, Jun 10 2012 (: (Start):)
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| STATUS
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approved
editing
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#17 by Jon E. Schoenfield at Thu Aug 17 02:48:24 EDT 2017
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#16 by Jon E. Schoenfield at Thu Aug 17 02:48:22 EDT 2017
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| FORMULA
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a(n) = (1/2)*sumSum_{j=1..m+1} (floor(n/10^j + 2/5)*(2n + 2 - (1/5 + floor(n/10^j + 2/5))*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)*A102677(n) + (1/2)*sumSum_{j=1..m+1} ((-1/5*floor(n/10^j + 2/5) + floor(n/10^j))*10^j - (floor(n/10^j + 2/5)^2 - floor(n/10^j)^2)*10^j), where m= = floor(log_10(n)).
G.f.: g(x) = (1/(1-x)^2)*sumSum_{j>=0} (x^(6*10^j) - x^(10*10^j))/(1- - x^10^(j+1)). (End)
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| MAPLE
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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]>=6 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i), i=0..n), n=0..86); (_); # _Emeric Deutsch_)_, Feb 23 2005
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| STATUS
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approved
editing
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#15 by N. J. A. Sloane at Mon Nov 04 21:48:40 EST 2013
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#14 by Jon E. Schoenfield at Mon Nov 04 21:07:03 EST 2013
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#13 by Jon E. Schoenfield at Mon Nov 04 21:07:01 EST 2013
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| COMMENTS
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The total number of digits >= 6 occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - ). - _Hieronymus Fischer, _, Jun 10 2012
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| MAPLE
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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]>=6 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(add(p(i), i=0..n), n=0..86); (); (_Emeric Deutsch)_)
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| STATUS
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approved
editing
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#12 by N. J. A. Sloane at Sun Nov 03 17:01:01 EST 2013
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| FORMULA
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Contribution from _Hieronymus Fischer, _, Jun 10 2012 (Start):
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Discussion
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| Sun Nov 03
| 17:01
| OEIS Server: https://oeis.org/edit/global/2040
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#11 by N. J. A. Sloane at Wed May 01 21:12:45 EDT 2013
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| EXTENSIONS
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An incorrect g.f. was deleted by _N. J. A. Sloane, _, Sep 16 2009
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Discussion
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| Wed May 01
| 21:12
| OEIS Server: https://oeis.org/edit/global/1902
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