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 A045523 #22 Jan 05 2025 19:51:35 %S A045523 8,12,26,53,57,73,82,118,129,155,160,169,185,212,215,218,232,240,265, %T A045523 272,281,294,338,351,369,376,388,393,398,403,408,421,432,443,446,482, %U A045523 485,498,515,522,533,544,548,576,580,593,602,616,621,641,646,657,668 %N A045523 Numbers k such that k! has initial digit '4'. %C A045523 The asymptotic density of this sequence is log_10(5/4) = 0.096910... (Kunoff, 1987). - _Amiram Eldar_, Jul 17 2020 %H A045523 Chai Wah Wu, <a href="/A045523/b045523.txt">Table of n, a(n) for n = 1..10000</a> %H A045523 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 A045523 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %F A045523 A008905(a(n)) = 4. - _Amiram Eldar_, Jul 17 2020 %e A045523 8 is a term since 8! = 40320 has the initial digit 4. %t A045523 Select[ Range[ 700 ], IntegerDigits[ #! ] [[ 1 ]] == 4 & ] %o A045523 (PARI) isok(n) = digits(n!)[1] == 4; \\ _Michel Marcus_, Feb 07 2017 %Y A045523 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. %K A045523 nonn,base %O A045523 1,1 %A A045523 _Jeff Burch_