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A045523 Numbers k such that k! has initial digit '4'. 18
8, 12, 26, 53, 57, 73, 82, 118, 129, 155, 160, 169, 185, 212, 215, 218, 232, 240, 265, 272, 281, 294, 338, 351, 369, 376, 388, 393, 398, 403, 408, 421, 432, 443, 446, 482, 485, 498, 515, 522, 533, 544, 548, 576, 580, 593, 602, 616, 621, 641, 646, 657, 668 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is log_10(5/4) = 0.096910... (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)) = 4. - Amiram Eldar, Jul 17 2020
EXAMPLE
8 is a term since 8! = 40320 has the initial digit 4.
MATHEMATICA
Select[ Range[ 700 ], IntegerDigits[ #! ] [[ 1 ]] == 4 & ]
PROG
(PARI) isok(n) = digits(n!)[1] == 4; \\ 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: A367894 A210982 A067677 * A006983 A283148 A072327
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified July 20 15:01 EDT 2024. Contains 374459 sequences. (Running on oeis4.)