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 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-François 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

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