A254717 a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 9's.

0, 12, 11, 36, 99, 207, 629, 3982, 13216, 24090, 65698, 131076, 176801, 2074822, 5203944, 3716991

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Example

a(1) = 12 since 12! = 479001600 contains '9' and 12 is the smallest integer for which the condition is met,
a(2) = 11 since 11! = 39916800 contains '99' and 11 is the smallest integer for which the condition is met.

Mathematica

A254717[n_] := Module[{m = 0},
   If[n == 0, While[MemberQ[IntegerDigits[m!], 9], m++]; m,
    t = Table[9, n];
    While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]];
Table[A254717[n], {n, 0, 7}] (* Robert Price, Mar 21 2019 *)

Prog

(PARI) a(n)=k=0; while(k<10^4, d=digits(2*10^(#(digits(k!))+1)+10*k!); for(j=1, #d-n+1, c=0; for(i=j, j+n-1, if(d[i]==9, c++); if(d[i]!=9, c=0; break)); if(c==n&&d[j+n]!=9&&d[j-1]!=9, return(k))); if(c==n, return(k)); if(c!=n, k++))
for(n=1, 6, print1(a(n), ", ")) \\ Derek Orr, Feb 06 2015

Crossrefs

Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254716.

Sequence in context: A086045 A072220 A171986 * A195748 A038337 A155825

Adjacent sequences: A254714 A254715 A254716 * A254718 A254719 A254720

Keyword

nonn,more,base

Author

Martin Y. Champel, Feb 06 2015

Extensions

a(12) from Jon E. Schoenfield, Feb 21 2015

a(13)-a(15) from Bert Dobbelaere, Oct 29 2018

Status

approved