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 A045521 #20 Jan 05 2025 19:51:35 %S A045521 2,4,16,20,23,30,32,34,39,44,47,54,58,68,75,85,86,87,113,114,115,126, %T A045521 135,142,148,153,159,163,168,172,180,184,188,195,205,208,211,214,217, %U A045521 220,223,226,234,237,242,247,252,257,262,269,276,278,287,289,302,304 %N A045521 Numbers k such that k! has initial digit '2'. %C A045521 The asymptotic density of this sequence is log_10(3/2) = 0.176091... (see A154580) (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020 %H A045521 Chai Wah Wu, <a href="/A045521/b045521.txt">Table of n, a(n) for n = 1..10000</a> %H A045521 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 A045521 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %F A045521 A008905(a(n)) = 2. - _Amiram Eldar_, Jul 17 2020 %e A045521 4 is a term since 4! = 24 has the initial digit 2. %t A045521 Select[ Range[ 310 ], IntegerDigits[ #! ] [ [ 1 ] ] == 2 & ] %o A045521 (PARI) isok(n) = digits(n!)[1] == 2; \\ _Michel Marcus_, Feb 07 2017 %Y A045521 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, A154580. %K A045521 nonn,base %O A045521 1,1 %A A045521 _Jeff Burch_ %E A045521 Offset changed to 1 by _Chai Wah Wu_, Feb 07 2017