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A045521
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Numbers k such that k! has initial digit '2'.
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18
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2, 4, 16, 20, 23, 30, 32, 34, 39, 44, 47, 54, 58, 68, 75, 85, 86, 87, 113, 114, 115, 126, 135, 142, 148, 153, 159, 163, 168, 172, 180, 184, 188, 195, 205, 208, 211, 214, 217, 220, 223, 226, 234, 237, 242, 247, 252, 257, 262, 269, 276, 278, 287, 289, 302, 304
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is log_10(3/2) = 0.176091... (see A154580) (Kunoff, 1987). - Amiram Eldar, Jul 17 2020
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LINKS
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FORMULA
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EXAMPLE
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4 is a term since 4! = 24 has the initial digit 2.
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MATHEMATICA
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Select[ Range[ 310 ], IntegerDigits[ #! ] [ [ 1 ] ] == 2 & ]
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PROG
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(PARI) isok(n) = digits(n!)[1] == 2; \\ Michel Marcus, Feb 07 2017
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CROSSREFS
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For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A008905, A154580.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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