

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.


10



0, 11, 9, 16, 27, 482, 532, 4731, 2061, 22402, 50381, 187611, 757618, 591042, 5157267, 9003765
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OFFSET

0,2


COMMENTS



LINKS



EXAMPLE

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.


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 *)


PROG

(PARI)
a(n)=k=0; while(k<10^4, d=digits(2*10^(#(digits(k!))+1)+10*k!); for(j=1, #dn+1, c=0; for(i=j, j+n1, if(d[i]==8, c++); if(d[i]!=8, c=0; break)); if(c==n&&d[j+n]!=8&&d[j1]!=8, return(k))); if(c==n, return(k)); if(c!=n, k++))
for(n=1, 6, print1(a(n), ", ")) \\ Derek Orr, Feb 06 2015


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS

a(12), a(13) from Jon E. Schoenfield, Mar 09 2015


STATUS

approved



