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 A214048 #15 Jun 19 2024 02:03:54
%S A214048 1,2,4,7,10,14,18,23,27,32,37,42,47,53,58,64,70,76,82,88,95,101,108,
%T A214048 114,121,128,135,142,149,156,163,170,177,185,192,199,207,214,222,230,
%U A214048 237,245,253,261,269,277,285,293,301,309
%N A214048 Least m>0 such that n! <= r^m, where r = (1+sqrt(5))/2, the golden ratio.
%C A214048 Also, the least m>0 such that n! < L(m), where L = A000032, the Lucas numbers.
%H A214048 Clark Kimberling, <a href="/A214048/b214048.txt">Table of n, a(n) for n = 1..1000</a>
%H A214048 Aleksandar Petojević, <a href="https://www.researchgate.net/publication/367253399_Lambert's_W_function_and_Kurepa's_left_factorial">Lambert's W function and Kurepa's left factorial</a>, Project: Kurepa's hypothesis for left factorial, ResearchGate (2023).
%H A214048 Aleksandar Petojević, Marjana Gorjanac Ranitović, Dragan Rastovac, and Milinko Mandić, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Petojevic/peto5.html">The Golden Ratio, Factorials, and the Lambert W Function</a>, Journal of Integer Sequences, Vol. 27 (2024), Article 24.5.7.
%e A214048 a(4) = 7 because r^6 < 4! <= 4^7.
%t A214048 Table[m=1; While[n!>GoldenRatio^m, m++]; m, {n,1,100}]
%Y A214048 Cf. A000032, A001622, A003070, A213857, A214047.
%K A214048 nonn,easy
%O A214048 1,2
%A A214048 _Clark Kimberling_, Jul 18 2012