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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

Table of n, a(n) for n=0..16.

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.)