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A112765 Exponent of highest power of 5 dividing n. Or, 5-adic valuation of n. 31
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

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 A083915 A083892

Adjacent sequences:  A112762 A112763 A112764 * A112766 A112767 A112768

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Sep 18 2005

STATUS

approved

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Last modified September 20 16:22 EDT 2017. Contains 292276 sequences.