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 A104114 #26 Jun 27 2025 21:41:29 %S A104114 1,2,6,24,48,432,1296,82944,165888,1088391168,3265173504 %N A104114 The order of the smallest solvable group with derived length n. %C A104114 At order 24, the two groups which achieve the maximum derived length are S_4 and SL(2,3). At order 48, a group which achieves the maximum derived length is GL(2,3). At order 432, the only group which achieves the maximum derived length is 3^2:GL(2,3). %C A104114 There are three groups of order 1296 achieving maximal derived length. - _Charles R Greathouse IV_, May 26 2014 %F A104114 a(n) >= 2*a(n-1). - _Charles R Greathouse IV_, May 26 2014 %e A104114 a_2=6 because the smallest solvable group with derived length 2 is the symmetric group S_3, which has order 6. %o A104114 (GAP) a := function(arg) %o A104114 local n, size, gr; %o A104114 n := arg[1]; %o A104114 if Length(arg) > 1 then %o A104114 size := arg[2]; %o A104114 else %o A104114 size := 1; %o A104114 fi; %o A104114 gr := OneSmallGroup(Size, size, DerivedLength, n); %o A104114 if gr <> fail then %o A104114 return size; %o A104114 else %o A104114 return a(n, size + 1); %o A104114 fi; %o A104114 end; # _Charles R Greathouse IV_, May 23 2014 %K A104114 nice,nonn,hard,more %O A104114 0,2 %A A104114 _David L. Harden_, Mar 31 2005 %E A104114 a(6) from _Charles R Greathouse IV_, May 26 2014 %E A104114 a(7)-a(10) from _Des MacHale_, Jun 26 2025