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.
0, 11, 9, 16, 27, 482, 532, 4731, 2061, 22402, 50381, 187611, 757618, 591042, 5157267, 9003765
Offset: 0
Examples
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.) a(2) = 9 since 9! = 362880 contains '88' and 9 is the smallest integer for which this condition is met.
Programs
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Mathematica
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 *) -
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]==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++)) for(n=1,6,print1(a(n),", ")) \\ Derek Orr, Feb 06 2015
Extensions
a(0)=0 added by M. F. Hasler, Feb 10 2015
a(11) from Jon E. Schoenfield, Feb 21 2015
a(13) from Jon E. Schoenfield, Feb 28 2015
a(12) from Jon E. Schoenfield, Mar 09 2015
a(14)-a(15) from Bert Dobbelaere, Oct 29 2018