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A007845
Least positive integer k for which 5^n divides k!.
7
1, 5, 10, 15, 20, 25, 25, 30, 35, 40, 45, 50, 50, 55, 60, 65, 70, 75, 75, 80, 85, 90, 95, 100, 100, 105, 110, 115, 120, 125, 125, 125, 130, 135, 140, 145, 150, 150, 155, 160, 165, 170, 175, 175, 180, 185, 190, 195, 200, 200, 205, 210, 215, 220, 225, 225, 230, 235, 240, 245
OFFSET
0,2
COMMENTS
Also the smallest factorial having at least n trailing zeros. - Jud McCranie, Oct 05 2010
a(n) ~ 4n, a(n) > 4n. Every positive multiple of 5 occurs as much as the exponent of 5 in the prime factorization. - David A. Corneth, Jul 12 2016
Least k such that A027868(k) >= n. - Robert Israel, Jul 12 2016
See A007843 and A007844 for the analog for 2 and 3 instead of 5. - M. F. Hasler, Dec 27 2019
REFERENCES
H. Ibstedt, Smarandache Primitive Numbers, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 216-229.
FORMULA
a(n) = 5*A228297(n) for n > 0: see A007843. - M. F. Hasler, Dec 27 2019
MAPLE
1, seq(t $ padic:-ordp(t, 5), t=5..1000, 5); # Robert Israel, Jul 12 2016
MATHEMATICA
lpi[n_]:=Module[{k=1, n5=5^n}, While[!Divisible[k!, n5], k++]; k]; Array[ lpi, 60, 0] (* Harvey P. Dale, Jun 19 2012 *)
PROG
(PARI) a(n) = {k = 1; while (valuation(k!, 5) < n, k++); k; } \\ Michel Marcus, Aug 19 2013
(PARI) a(n) = {my(ck = 4 * n, k = 5 * floor(ck/5), t = 0); if(ck > 0, t = sum(i = 1, logint(ck, 5), ck\=5)); while(t < n, k+=5; t+=valuation(k, 5)); max(1, k)} \\ David A. Corneth, Jul 12 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Bruce Dearden and Jerry Metzger
STATUS
approved