A102669 Number of digits >= 2 in decimal representation of n.

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

Offset

0,23

Comments

a(n) = 0 iff n is in A007088 (numbers in base 2). - Bernard Schott, Feb 19 2023

Links

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

Formula

Contribution from Hieronymus Fischer, Jun 10 2012: (Start)

a(n) = Sum_{j=1..m+1} (floor(n/10^j + 4/5) - floor(n/10^j)), where m = floor(log_10(n)).

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(2*10^j) - x^(10*10^j))/(1 - x^10^(j+1)).

General formulas for the number of digits >= d in the decimal representations of n, where 1 <= d <= 9:

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

G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(d*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (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]>=2 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n), n=0..116); # Emeric Deutsch, Feb 23 2005

Mathematica

Table[Total@ Take[DigitCount@ n, {2, 9}], {n, 0, 104}] (* Michael De Vlieger, Aug 17 2017 *)

Crossrefs

Cf. A027868, A054899, A055640, A055641, A102670 - A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102670.

Cf. A000120, A000788, A007088, A023416, A059015 (for base 2).

Sequence in context: A194322 A052010 A138471 * A248327 A055098 A297035

Adjacent sequences: A102666 A102667 A102668 * A102670 A102671 A102672

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 03 2005

Extensions

More terms from Emeric Deutsch, Feb 23 2005

Status

approved