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 A363746 #30 Feb 16 2025 08:34:05 %S A363746 1,1,4,7,2 %N A363746 Initial digit of the decimal expansion of the tetration n^^n (in Don Knuth's up-arrow notation). %C A363746 a(5), the most significant digit of the tetration 5^^5, has been estimated to be equal to 1 (and this is also consistent with Benford's law), but there is not any strict proof at the present time and computers are not powerful enough to calculate it without uncertainty. %H A363746 Allam's Numbers, <a href="https://sites.google.com/site/allamsnumbers/home/part-2/hyperoperational-numbers/digits-of-tetrational-numbers">Digits of tetrational numbers</a> %H A363746 A. Bogomolny, <a href="http://www.cut-the-knot.org/do_you_know/zipfLaw.shtml">Benford's Law and Zipf's Law</a>, Cut the Knot.org. %H A363746 Googology, <a href="https://googology.fandom.com/wiki/Tetration">Tetration</a>. %H A363746 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JoyceSequence.html">Joyce Sequence</a>. %H A363746 Wikipedia, <a href="http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation">Knuth's up-arrow notation</a>. %F A363746 a(n) = floor(n^^n/10^floor(log_10(n^^n))). %F A363746 a(n) = A000030(A004231(n)). %e A363746 a(3) = 7 since 3^^3 = 7625597484987. %Y A363746 Cf. A000030, A004231 (n^^n), A241293 (4^^4 digits). %Y A363746 Cf. A241299, A244059, A362004. %K A363746 base,hard,more,nonn %O A363746 0,3 %A A363746 _Marco Ripà_, Jun 19 2023