A160093 Number of digits in n, excluding any trailing zeros.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3

Offset: 1

Author

Anonymous, May 01 2009

Keywords

• base
• easy
• nonn

Examples

			a(1060000) = 3 because discarding the trailing zeros from 1060000 leaves 106, which is a 3-digit number.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004151, A054899, A055640, A055641, A055642, A102669, A122840, A122841, A160094, A196563, A196564.

Programs

Mathematica

lnzd[n_]:=Module[{spl=Last[Split[IntegerDigits[n]]]},If[!MemberQ[ spl,0], IntegerLength[n], IntegerLength[n]-Length[spl]]]; Array[lnzd,110] (* Harvey P. Dale, Jun 05 2013 *)
Table[IntegerLength[n] - IntegerExponent[n, 10], {n, 100}] (* Amiram Eldar, Sep 14 2020 *)

PARI

a(n)=if(n==0,1,#digits(n/10^valuation(n,10))) \\ Joerg Arndt, Jan 11 2017

PARI

a(n)=logint(n,10)+1-valuation(n,10) \\ Charles R Greathouse IV, Jan 12 2017

Python

def A160093(n):
     return len(str(int(str(n)[::-1]))) # Indranil Ghosh, Jan 11 2017

Formula

From Hieronymus Fischer, Jun 08 2012: (Start)

With m = floor(log_10(n)), frac(x) = x-floor(x):

a(n) = 1 + Sum_{j=0..m} ceiling(frac(n/10^j)).

a(n) = 1 - Sum_{j=1..m} (floor(-frac(n/10^j))).

a(n)= A055642(n) + A054899(n-1) - A054899(n).

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

a(n) = A055642(A004086(n)). - Indranil Ghosh, Jan 11 2017

a(n) = A055642(A004151(n)). - Amiram Eldar, Sep 14 2020

Extensions

Simpler definition and changed example from Jon E. Schoenfield, Feb 15 2014