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

0,2

Comments

a(13)=591042. - Jon E. Schoenfield, Feb 28 2015

Links

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

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, #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

Crossrefs

Cf. A254042, A254447, A254448, A254449, A254500, A254501, A254502, A254717.

Sequence in context: A004500 A342162 A337227 * A240757 A206422 A316450

Adjacent sequences: A254713 A254714 A254715 * A254717 A254718 A254719

Keyword

nonn,base,more

Author

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

a(14)-a(15) from Bert Dobbelaere, Oct 29 2018

Status

approved