|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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.
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|