login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A112765 Exponent of highest power of 5 dividing n. Or, 5-adic valuation of n. 35
0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,25

COMMENTS

A027868 gives partial sums.

This is also the 5-adic valuation of Fibonacci(n). See Lengyel link. - Michel Marcus, May 06 2017

LINKS

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

T. Lengyel, The order of the Fibonacci and Lucas numbers, Fibonacci Quart. 33 (1995), no. 3, 234-239. See Lemma 1 p. 235.

FORMULA

Totally additive with a(p) = 1 if p = 5, 0 otherwise.

From Hieronymus Fischer, Jun 08 2012 (Start):

With m = floor(log_5(n)), frac(x) = x-floor(x):

a(n) = Sum_{j=1..m} (1 - ceiling(frac(n/5^j))).

a(n) = m + Sum_{j=1..m} (floor(-frac(n/5^j))).

a(n)= A027868(n) - A027868(n-1).

G.f.: Sum_{j>0} x^5^j/(1-x^5^j). (End)

a(5n) = A055457(n). - R. J. Mathar, Jul 17 2012

MAPLE

A112765 := proc(n)

    padic[ordp](n, 5) ;

end proc: # R. J. Mathar, Jul 12 2016

MATHEMATICA

a[n_] := IntegerExponent[n, 5]; Array[a, 105] (* Jean-Fran├žois Alcover, Jan 25 2018 *)

PROG

(Haskell)

a112765 n = fives n 0 where

   fives n e | r > 0     = e

             | otherwise = fives n' (e + 1) where (n', r) = divMod n 5

-- Reinhard Zumkeller, Apr 08 2011

(PARI) A112765(n)=valuation(n, 5); /* Joerg Arndt, Apr 08 2011 */

CROSSREFS

Cf. A007814, A007949, A112762, A022337, A122840, A027868, A054899, A122841 A160093, A160094, A196563, A196564.

Sequence in context: A073345 A216511 A138088 * A105966 A318950 A319000

Adjacent sequences:  A112762 A112763 A112764 * A112766 A112767 A112768

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Sep 18 2005

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 19 06:03 EST 2018. Contains 318245 sequences. (Running on oeis4.)