A102683 Number of digits 9 in decimal representation of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0

Offset

0,100

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(A007095(n)) = 0; a(A011539(n)) > 0. - Reinhard Zumkeller, Dec 29 2011

From Hieronymus Fischer, Jun 10 2012: (Start)

a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/10) - floor(n/10^j)), where m=floor(log_10(n)).

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(9*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

a(A235049(n)) = 0. - Reinhard Zumkeller, Apr 16 2014

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]>=9 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n), n=0..116); # Emeric Deutsch, Feb 23 2005

Mathematica

a[n_] := DigitCount[n, 10, 9]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

Prog

(Haskell)
a102683 =  length . filter (== '9') . show
-- Reinhard Zumkeller, Dec 29 2011

Crossrefs

Cf. A007095, A011539, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564, A235049.

Cf. A102684 (partial sums).

Cf. A000120, A000788, A023416, A059015 (for base 2).

Sequence in context: A062892 A118553 A102448 * A122840 A379671 A083919

Adjacent sequences: A102680 A102681 A102682 * A102684 A102685 A102686

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 03 2005

Extensions

More terms from Emeric Deutsch, Feb 23 2005

Status

approved