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a(n) is the smallest nonnegative integer such that a(n)! contains a string of exactly n consecutive 9's.
11

%I #20 Mar 21 2019 13:32:11

%S 0,12,11,36,99,207,629,3982,13216,24090,65698,131076,176801,2074822,

%T 5203944,3716991

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

%e a(1) = 12 since 12! = 479001600 contains '9' and 12 is the smallest integer for which the condition is met,

%e a(2) = 11 since 11! = 39916800 contains '99' and 11 is the smallest integer for which the condition is met.

%t A254717[n_] := Module[{m = 0},

%t If[n == 0, While[MemberQ[IntegerDigits[m!], 9], m++]; m,

%t t = Table[9, n];

%t While[! MemberQ[Split[IntegerDigits[m!]], t], m++]; m]];

%t Table[A254717[n], {n, 0, 7}] (* _Robert Price_, Mar 21 2019 *)

%o (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++))

%o for(n=1,6,print1(a(n),", ")) \\ _Derek Orr_, Feb 06 2015

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

%K nonn,more,base

%O 0,2

%A _Martin Y. Champel_, Feb 06 2015

%E a(12) from _Jon E. Schoenfield_, Feb 21 2015

%E a(13)-a(15) from _Bert Dobbelaere_, Oct 29 2018