A072208 - OEIS

A072208

a(n)-th factorial is the smallest factorial containing exactly n 8's, or 0 if no such number exists.

11, 9, 36, 16, 30, 27, 39, 33, 44, 58, 56, 64, 80, 70, 72, 94, 97, 71, 108, 143, 120, 134, 118, 162, 125, 133, 151, 137, 138, 159, 169, 197, 184, 171, 178, 176, 206, 177, 191, 208, 207, 240, 252, 232, 239, 270, 229, 308, 243, 223, 278, 257, 250, 0, 303, 242, 311

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OFFSET

1,1

COMMENTS

It is conjectured that a(54)=0 since no factorial < 10000 contained just 54 eights.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

a(2)=9 since 9th factorial i.e. 9!=362880 contains exactly two 8's.

MATHEMATICA

Do[k = 1; While[ Count[IntegerDigits[k! ], 8] != n, k++ ]; Print[k], {n, 1, 60}]

Transpose[Flatten[Table[Select[Table[{n, DigitCount[n!, 10, 8]}, {n, 500}], Last[#] == i&, 1], {i, 50}], 1]][[1]] (* Harvey P. Dale, Sep 13 2013 *)