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A045525
Numbers k such that k! has initial digit '6'.
18
3, 13, 18, 24, 43, 49, 72, 120, 130, 138, 174, 178, 182, 193, 203, 227, 263, 270, 290, 309, 311, 313, 315, 317, 319, 321, 355, 364, 371, 378, 390, 395, 400, 405, 418, 426, 437, 457, 460, 463, 466, 469, 491, 501, 511, 518, 525, 536, 555, 559, 563, 567, 571
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is log_10(7/6) = 0.066946... (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)) = 6. - Amiram Eldar, Jul 17 2020
EXAMPLE
3 is a term since 3! = 6 has the initial digit 6.
MATHEMATICA
Select[ Range[ 600 ], IntegerDigits[ #! ] [ [1] ] == 6 & ]
PROG
(PARI) isok(n) = digits(n!)[1] == 6; \\ Michel Marcus, Feb 08 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: A273946 A070518 A263182 * A030774 A024685 A024474
KEYWORD
nonn,base
AUTHOR
STATUS
approved