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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 (list; graph; refs; listen; history; text; internal format)
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('[0-9]*[1-9]0{'+str(n)+'}[1-9][0-9]*')

    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

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Last modified September 29 20:22 EDT 2020. Contains 337432 sequences. (Running on oeis4.)