

A045521


Numbers k such that k! has initial digit '2'.


18



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

1,1


COMMENTS

The asymptotic density of this sequence is log_10(3/2) = 0.176091... (see A154580) (Kunoff, 1987).  Amiram Eldar, Jul 17 2020


LINKS



FORMULA



EXAMPLE

4 is a term since 4! = 24 has the initial digit 2.


MATHEMATICA

Select[ Range[ 310 ], IntegerDigits[ #! ] [ [ 1 ] ] == 2 & ]


PROG

(PARI) isok(n) = digits(n!)[1] == 2; \\ Michel Marcus, Feb 07 2017


CROSSREFS

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.


KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



