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A072178
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a(n)-th factorial is the smallest factorial containing exactly n 4's, or 0 if no such number exists.
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8
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4, 19, 21, 24, 44, 42, 50, 57, 0, 60, 76, 91, 56, 86, 85, 66, 92, 88, 114, 129, 131, 106, 130, 122, 117, 157, 134, 175, 119, 150, 181, 165, 185, 179, 198, 182, 220, 228, 188, 190, 261, 235, 222, 231, 229, 233, 224, 227, 288, 372, 241, 279, 254, 253, 318, 267
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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(9) = 0 since no factorial < 10000 contained just 9 fours.
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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) = 19 since 19th factorial, i.e., 19! = 121645100408832000 contains exactly two 4's.
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MATHEMATICA
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Do[k = 1; While[ Count[IntegerDigits[k! ], 4] != n, k++ ]; Print[k], {n, 1, 60}]
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PROG
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(Python)
from math import factorial
def a(n, limit=1000):
fact = 1
for t in range(limit+1):
if str(fact).count('4') == n: return t
fact *= (t+1)
return 0
print([a(n) for n in range(1, 57)]) # Michael S. Branicky, Apr 19 2021
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CROSSREFS
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Cf. A072244, A072220, A072208, A072204, A072200, A072199, A072177, A072163, A072124.
Sequence in context: A165820 A043056 A012879 * A116980 A296602 A022135
Adjacent sequences: A072175 A072176 A072177 * A072179 A072180 A072181
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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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