OFFSET
1,100
COMMENTS
Greatest k such that 10^k divides n.
a(n) = the number of digits in n - A160093(n).
a(A005117(n)) <= 1. - Reinhard Zumkeller, Mar 30 2010
See A054899 for the partial sums. - Hieronymus Fischer, Jun 08 2012
From Amiram Eldar, Mar 10 2021: (Start)
The asymptotic density of the occurrences of k is 9/10^(k+1).
The asymptotic mean of this sequence is 1/9. (End)
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
S. Ikeda and K. Matsuoka, On transcendental numbers generated by certain integer sequences, Siauliai Math. Semin., 8 (16) 2013, 63-69.
FORMULA
a(n) = A160094(n) - 1.
From Hieronymus Fischer, Jun 08 2012: (Start)
With m = floor(log_10(n)), frac(x) = x-floor(x):
a(n) = Sum_{j=1..m} (1 - ceiling(frac(n/10^j))).
a(n) = m + Sum_{j=1..m} (floor(-frac(n/10^j))).
G.f.: g(x) = Sum_{j>0} x^10^j/(1-x^10^j). (End)
EXAMPLE
a(160) = 1 because there is 1 zero at the end of 160 when 160 is written in base 10.
MATHEMATICA
a[n_] := IntegerExponent[n, 10]; Array[a, 100] (* Amiram Eldar, Mar 10 2021 *)
PROG
(Haskell)
a122840 n = if n < 10 then 0 ^ n else 0 ^ d * (a122840 n' + 1)
where (n', d) = divMod n 10
-- Reinhard Zumkeller, Mar 09 2013
(PARI) a(n)=valuation(n, 10) \\ Charles R Greathouse IV, Feb 26 2014
(Python)
def a(n): return len(str(n)) - len(str(int(str(n)[::-1]))) # Indranil Ghosh, Jun 09 2017
(Python)
def A122840(n): return len(s:=str(n))-len(s.rstrip('0')) # Chai Wah Wu, Jul 06 2022
(Python)
A122840 = lambda n: sympy.multiplicity(10, n) # M. F. Hasler, Apr 05 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Reinhard Zumkeller, Sep 13 2006
STATUS
approved