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

0,56

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

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)

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 *)

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).

Sequence in context: A345112 A063059 A214564 * A177849 A143544 A031346

Adjacent sequences: A102672 A102673 A102674 * A102676 A102677 A102678

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 03 2005

Extensions

More terms from Emeric Deutsch, Feb 23 2005

Status

approved