A072220 a(n)-th factorial is the smallest factorial containing exactly n 9's, or 0 if no such number exists.

12, 11, 21, 29, 34, 46, 36, 59, 79, 75, 0, 70, 82, 90, 95, 97, 112, 89, 105, 96, 134, 130, 127, 165, 142, 149, 144, 145, 161, 163, 182, 189, 160, 178, 139, 180, 206, 192, 224, 214, 188, 215, 226, 207, 218, 267, 283, 261, 268, 262, 240, 280, 234, 285, 343, 277

Offset

1,1

Comments

It is conjectured that a(11) = 0 since no factorial < 10000 contains exactly eleven nines.

Links

Table of n, a(n) for n=1..56.

Example

a(2) = 11 since 11! = 39916800 contains exactly two 9's.

Mathematica

Do[k = 1; While[ Count[IntegerDigits[k! ], 9] != n, k++ ]; Print[k], {n, 1, 60}]
Module[{c=Table[{n, DigitCount[n!, 10, 9]}, {n, 350}]}, Table[SelectFirst[c, #[[2]]==m&], {m, 60}]][[;; , 1]]/."NotFound"->0 (* Harvey P. Dale, Sep 18 2023 *)

Prog

(Python)
def a(n, multiple_limit=300):
    fk, limit = 1, multiple_limit*n
    for k in range(1, limit+1):
        fk *= k
        if str(fk).count("9") == n: return k
    return 0
print([a(n) for n in range(1, 57)]) # Michael S. Branicky, Dec 11 2021

Crossrefs

Cf. A072232, A072208, A072204, A072200, A072199, A072178, A072177, A072163, A072124.

Sequence in context: A358497 A019330 A086045 * A171986 A254717 A195748

Adjacent sequences: A072217 A072218 A072219 * A072221 A072222 A072223

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 30 2002

Extensions

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

Status

approved