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 A372970 #20 May 19 2024 13:16:58 %S A372970 1,2,1,2,2,3,2,4,2,5,2,4,3,4,3,4,4,4,4,4,4,5,4,6,4,6,4,7,4,7,4,8,4,8, %T A372970 4,9,4,9,4,10,4,10,4,8,5,9,5,8,6,8,6,8,6,9,6,8,7,8,7,8,7,8,7,8,8,8,8, %U A372970 8,8,8,8,8,8,9,8,8,8,9,8,8,8,10,8,8,8,10,8,11,8,11,8,10,9,10,9,10,9,10,9,11 %N A372970 a(1)=1, then a(n) = floor(n/max(a(n-1),a(floor(n/2)))). %C A372970 It seems that limsup and liminf of a(n)/sqrt(n) exist (see link). %H A372970 Benoit Cloitre, <a href="/A372970/a372970.png">Plot of a(n)/sqrt(n) for n=1 up to 400000</a>. %H A372970 Hugo Pfoertner, <a href="/A372970/a372970.pdf">Plot of a(n)/sqrt(n)</a>, n=1..400000, zoom into pdf to see details. %o A372970 (PARI) a(n)=if(n<2,1,floor(n/max(a(n-1),a(n\2)))) %Y A372970 Cf. A372971, A097051. %K A372970 nonn %O A372970 1,2 %A A372970 _Benoit Cloitre_, May 18 2024