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 A072220 a(n)-th factorial is the smallest factorial containing exactly n 9's, or 0 if no such number exists. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is conjectured that a(11) = 0 since no factorial < 10000 contains exactly eleven nines. LINKS 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}] 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

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)