cp's OEIS Frontend

A254716 a(n) is the smallest nonnegative integer m such that m! contains a string of exactly n consecutive 8's, or -1 if no such m exists.

%I A254716 #31 Sep 02 2025 23:31:28
%S A254716 0,11,9,16,27,482,532,4731,2061,22402,50381,187611,757618,591042,
%T A254716 5157267,9003765
%N A254716 a(n) is the smallest nonnegative integer m such that m! contains a string of exactly n consecutive 8's, or -1 if no such m exists.
%e A254716 a(1) = 11 since 11! = 39916800 contains '8' and 11 is the smallest integer for which the condition is met. (In 9! the '8's occur in a substring of length 2.)
%e A254716 a(2) = 9 since 9! = 362880 contains '88' and 9 is the smallest integer for which this condition is met.
%t A254716 f[n_] := Block[{k = 0, str = ToString[ 8(10^n - 1)/9]}, While[ Length@ StringPosition[ ToString[ k!], str] != 1, k++]; k]; f[0] = 0; Array[f, 14, 0] (* _Robert G. Wilson v_, Mar 10 2015 *)
%o A254716 (PARI)
%o A254716 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]==8, c++); if(d[i]!=8, c=0; break)); if(c==n&&d[j+n]!=8&&d[j-1]!=8, return(k))); if(c==n, return(k)); if(c!=n, k++))
%o A254716 for(n=1,6,print1(a(n),", ")) \\ _Derek Orr_, Feb 06 2015
%Y A254716 Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254717.
%K A254716 nonn,base,more,changed
%O A254716 0,2
%A A254716 _Martin Y. Champel_, Feb 06 2015
%E A254716 a(0)=0 added by _M. F. Hasler_, Feb 10 2015
%E A254716 a(11) from _Jon E. Schoenfield_, Feb 21 2015
%E A254716 a(13) from _Jon E. Schoenfield_, Feb 28 2015
%E A254716 a(12) from _Jon E. Schoenfield_, Mar 09 2015
%E A254716 a(14)-a(15) from _Bert Dobbelaere_, Oct 29 2018