This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A045528 #22 Jan 05 2025 19:51:35 %S A045528 96,97,98,99,100,101,102,103,122,139,166,190,233,241,261,268,301,331, %T A045528 366,380,415,431,445,481,497,514,521,583,596,624,629,634,655,672,690, %U A045528 716,723,762,789,799,821,833,861,897 %N A045528 Numbers k such that k! has initial digit '9'. %C A045528 The asymptotic density of this sequence is log_10(10/9) = 1 - log_10(9) = 0.045757... (A104140) (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020 %H A045528 Chai Wah Wu, <a href="/A045528/b045528.txt">Table of n, a(n) for n = 1..10000</a> %H A045528 Sharon Kunoff, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/25-4/kunoff.pdf">N! has the first digit property</a>, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367. %H A045528 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %F A045528 A008905(a(n)) = 9. - _Amiram Eldar_, Jul 17 2020 %e A045528 96 is a term since 96! = 9.916779... * 10^149 has the initial digit 9. %t A045528 Select[ Range[ 900 ], IntegerDigits[ #! ] [ [1] ] == 9 & ] %o A045528 (PARI) isok(n) = digits(n!)[1] == 9; \\ _Michel Marcus_, Feb 08 2017 %Y A045528 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, A104140. %K A045528 nonn,base %O A045528 1,1 %A A045528 _Jeff Burch_ %E A045528 More terms from _Robert G. Wilson v_, Jan 03 2001