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 A255400 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 0's. 1
 0, 5, 10, 15, 20, 264, 25, 30, 35, 40, 45, 101805, 50, 55, 60, 65, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Most multiples of 5 belong to the sequence (if not all). All terms whose indices are included in A000966 are far bigger than their neighboring terms whose indices are multiples of 5. a(11) is a multiple of 5, we can verify a(11) = a(25448). LINKS EXAMPLE a(0) = 0 as 0! = 1 does not contain '0'. a(1) = 5 as 5! = 120 contains '0'. a(2) = 10 as 10! = 3628800 contains '00' and 10 is the smallest integer for which the condition is met. PROG (Python 2.7) from math import factorial as fct .... def trailing_zero(n): ....k=0 ....while n!=0: ........n/=5 ........k+=n ....return k .... def A255400(): ....index = 1 ....f = 1 ....while True: ........if trailing_zero(f) == index: ............print "A255400("+str(index)+") = " +str(f) ............index += 1 ........elif trailing_zero(f) > index: ............while True: ................clnzer = str(fct(f))[:-trailing_zero(f)] ................if index*'0' in clnzer and (index+1)*'0' not in clnzer: ....................print "A255400("+str(index)+") = " +str(f) ....................index += 1 ....................f = 0 ....................break .............f +=1 ........f +=1 ....return (Python) import re def A255400(n): ....f, i, s = 1, 0, re.compile('[0-9]*[1-9]0{'+str(n)+'}[1-9][0-9]*') ....while s.match(str(f)+'1') == None: ........i += 1 ........f *= i ....return i # Chai Wah Wu, Apr 02 2015 CROSSREFS Cf. A027868, A000966. Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254716, A254717. Cf. A252652. Sequence in context: A070004 A104356 A137935 * A115182 A313762 A313763 Adjacent sequences:  A255397 A255398 A255399 * A255401 A255402 A255403 KEYWORD nonn,base,more AUTHOR Martin Y. Champel, Feb 22 2015 STATUS approved

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)