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A122840 a(n) is the number of 0s at the end of n when n is written in base 10. 39
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

REFERENCES

S. Ikeda, K. Matsuoka, On transcendental numbers generated by certain integer sequences, Siauliai Math. Semin., 8 (16) 2013, 63-69; http://siauliaims.su.lt/pdfai/2013/Iked-Mats-2013.pdf

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

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Last modified August 17 17:27 EDT 2017. Contains 290648 sequences.