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A045522
Numbers k such that k! has initial digit '3'.
18
9, 10, 11, 17, 28, 36, 41, 50, 62, 67, 74, 83, 84, 116, 117, 127, 128, 136, 143, 149, 154, 164, 173, 177, 181, 192, 199, 202, 229, 245, 250, 255, 260, 267, 274, 283, 285, 296, 298, 300, 332, 334, 336, 349, 358, 360, 367, 374, 381, 386, 411, 416, 424, 435, 449
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is log_10(4/3) = 0.124938... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020
LINKS
Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.
FORMULA
A008905(a(n)) = 3. - Amiram Eldar, Jul 17 2020
EXAMPLE
9 is a term since 9! = 362880 has the initial digit 3.
MATHEMATICA
Select[ Range[ 500 ], IntegerDigits[ #! ] [ [ 1 ] ] == 3 & ]
PROG
(PARI) isok(n) = digits(n!)[1] == 3; \\ 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.
Sequence in context: A086446 A168042 A342147 * A054967 A227801 A048031
KEYWORD
nonn,base
AUTHOR
STATUS
approved