A102681 Number of digits >= 8 in decimal representation of n.

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

Offset: 0

Author

N. J. A. Sloane, Feb 03 2005

Keywords

• nonn
• base
• easy

Comments

a(n) = 0 iff n is in A007094 (numbers in base 8). - Bernard Schott, Feb 18 2023

Links

• Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007094, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102682.

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

Programs

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]>=8 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..120); # Emeric Deutsch, Feb 23 2005

Formula

From Hieronymus Fischer, Jun 10 2012: (Start)

a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/5) - floor(n/10^j)), where m = floor(log_10(n)).

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(8*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

Extensions

More terms from Emeric Deutsch, Feb 23 2005