A102675 Number of digits >= 5 in decimal representation of n.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 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 A007091 (numbers in base 5). - Bernard Schott, Feb 02 2023

References

• Curtis Cooper, Number of large digits in the positive integers not exceeding n, Abstracts Amer. Math. Soc., 25 (No. 1, 2004), p. 38, Abstract 993-11-964.

Links

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

Crossrefs

Cf. A007091 (indices of 0's), A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564, A102676 (partial sums).

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]>=5 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..120); # Emeric Deutsch, Feb 23 2005

Mathematica

Table[Count[IntegerDigits[n],?(#>4&)],{n,0,120}] (* _Harvey P. Dale, Nov 13 2013 *)

Formula

From Hieronymus Fischer, Jun 10 2012: (Start)

a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/2) - floor(n/10^j)), where m = floor(log_10(n)).

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(5*10^j) - x^(10*10^j))/(1 - x^10^(j+1)).

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} x^(5*10^j)/(1 + x^(5*10^j)). (End)

Extensions

More terms from Emeric Deutsch, Feb 23 2005