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 A230863 #46 Sep 05 2024 15:43:58 %S A230863 0,1,2,4,8,16,64,256,4096,65536,16777216,4294967296, %T A230863 1208925819614629174706176,340282366920938463463374607431768211456, %U A230863 2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 %N A230863 a(1)=0; thereafter a(n) = 2^(a(ceiling(n/2)) + a(floor(n/2))). %C A230863 a(16) = 2^512 %C A230863 = 134078079299425970995740249982058461274793658205923933777235\ %C A230863 614437217640300735469768018742981669034276900318581864860508537538828119465\ %C A230863 69946433649006084096. %H A230863 Max A. Alekseyev and N. J. A. Sloane, <a href="https://arxiv.org/abs/2112.14365">On Kaprekar's Junction Numbers</a>, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155. %F A230863 In general, for n >= 11, define i by 9*2^(i-1) < n <= 9*2^i. Then it appears that a(n) = 2^2^2^...^2^x, a tower of height i+5, containing i+4 2's, where x is in the range 0 < x <= 1. %F A230863 For example, if n=18, i=1, and a(18) = 2^8192 = 2^2^2^2^2^0.91662699..., of height 6. %F A230863 Note also that i+5 = A230864(a(n)). %p A230863 f:=proc(n) option remember; %p A230863 if n=1 then 0 else 2^(f(ceil(n/2))+f(floor(n/2))); fi; end; %p A230863 [seq(f(n),n=1..16)]; %Y A230863 Cf. A230864, A230874, A230875. %K A230863 nonn %O A230863 1,3 %A A230863 _N. J. A. Sloane_, Nov 02 2013; revised Mar 26 2014