

A252652


a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 0's, not including trailing 0's.


4



0, 7, 12, 22, 107, 264, 812, 4919, 12154, 24612, 75705, 101805, 236441, 1946174
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..13.


EXAMPLE

a(0) = 0 since 0! = 1, which does not contain a 0.
a(1) = 7 since 7! = 5040, which contains a 0 other than the trailing 0, and no integer smaller than 7 satisfies this requirement. (a(1) is not 5; 5! = 120, which has no 0 digits other than the trailing 0.)
a(2) = 12 since 12! = 479001600; discarding the trailing 0's leaves 4790016, which contains a string of exactly two consecutive 0's, and no integer smaller than 12 satisfies this requirement.


MATHEMATICA

A252652[n_] := Module[{m = 0, s, t},
If[n == 0, While[MemberQ[IntegerDigits[m!], 0], m++]; m,
t = Table[0, n];
While[s = Split[IntegerDigits[m!]];
If[MemberQ[Last[s], 0], s = Delete[s, 1]]; ! MemberQ[s, t],
m++]; m]];
Table[A252652[n], {n, 0, 13}] (* Robert Price, Mar 21 2019 *)


PROG

(Python)
import re
def A252652(n):
if n == 0:
return 0
f, i, s = 1, 0, re.compile('[09]*[19]0{'+str(n)+'}[19][09]*')
while s.match(str(f)) == None:
i += 1
f *= i
return i # Chai Wah Wu, Dec 29 2015


CROSSREFS

Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254716, A254717.
Sequence in context: A273114 A273178 A160423 * A192752 A097925 A132195
Adjacent sequences: A252649 A252650 A252651 * A252653 A252654 A252655


KEYWORD

nonn,base,more


AUTHOR

Jon E. Schoenfield, Mar 22 2015, at the suggestion of Martin Y. Champel


EXTENSIONS

a(13) from Lars Blomberg, Apr 05 2015


STATUS

approved



