login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122840 a(n) is the number of 0's at the end of n when n is written in base 10. 40
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
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

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))).

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

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.

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

CROSSREFS

A007814 is the base 2 equivalent of this sequence.

Cf. A160094, A160093, A001511, A070940, A122841, A027868, A054899, A122840, A196563, A196564, A004151.

Sequence in context: A118553 A102448 A102683 * A083919 A063665 A276306

Adjacent sequences:  A122837 A122838 A122839 * A122841 A122842 A122843

KEYWORD

nonn,base,easy

AUTHOR

Reinhard Zumkeller, Sep 13 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 17:16 EST 2020. Contains 338954 sequences. (Running on oeis4.)