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%I #27 Jun 21 2022 19:56:57
%S 0,1,2,6,11,18,25,35,45,58,71,87,103
%N Diameter of symmetric group S_n when generated by (1,2) and (1,2,3,...,n).
%C a(n) is smallest number such that every element of S_n can be written as a product of at most a(n) terms each of which is the transposition (1,2) or the n-cycle (1,2,3,...,n).
%C The distinction between A039745 (this sequence) and A186783 comes from whether we treat the Cayley graph of the generating set as directed or undirected (alternatively, whether we allow multiplication by inverses of generators when constructing elements). A039745 deals with the directed Cayley graph, while A186783 deals with the undirected one. - _Max Alekseyev_, Sep 09 2011
%e a(3)=2 because (1,3,2) = (1,2,3)(1,2).
%t a[n_] := GraphDiameter[CayleyGraph[SymmetricGroup[n]]] (* _Ben Whitmore_, Nov 13 2020 *)
%o (Sage) def a(n): return PermutationGroup([[(1,2)],[tuple(1..n)]]).cayley_graph().diameter() # _Max Alekseyev_, Mar 02 2010
%Y See A186783 for another version.
%Y Cf. A186144
%K hard,nonn,nice,more
%O 1,3
%A _David desJardins_
%E a(12)-a(13) by _Ben Whitmore_, Nov 12 2020
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