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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 (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 Chai Wah Wu, Table of n, a(n) for n = 1..10000 Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367. Index entries for sequences related to factorial numbers 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 Adjacent sequences: A045519 A045520 A045521 * A045523 A045524 A045525 KEYWORD nonn,base AUTHOR Jeff Burch STATUS approved

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Last modified October 3 13:23 EDT 2023. Contains 365866 sequences. (Running on oeis4.)