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

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 *)

Crossrefs

Cf. A072237, A072220, A072204, A072200, A072199, A072178, A072177, A072163, A072124.

Sequence in context: A316450 A196006 A196003 * A210284 A219746 A335854

Adjacent sequences: A072205 A072206 A072207 * A072209 A072210 A072211

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 30 2002

Extensions

Edited and extended by Robert G. Wilson v, Jul 31 2002

Status

approved