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A072220
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a(n)-th factorial is the smallest factorial containing exactly n 9's, or 0 if no such number exists.
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8
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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
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OFFSET
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1,1
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COMMENTS
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It is conjectured that a(11) = 0 since no factorial < 10000 contains exactly eleven nines.
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LINKS
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Table of n, a(n) for n=1..56.
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EXAMPLE
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a(2) = 11 since 11! = 39916800 contains exactly two 9's.
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MATHEMATICA
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Do[k = 1; While[ Count[IntegerDigits[k! ], 9] != n, k++ ]; Print[k], {n, 1, 60}]
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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base,nonn
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AUTHOR
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Shyam Sunder Gupta, Jul 30 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v, Jul 31 2002
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STATUS
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approved
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