%I A138568
%S A138568 1,212,3212321,4321234321234,543212345432123454321,
%T A138568 6543212345654321234565432123456,
%U A138568 7654321234567654321234567654321234567654321
%N A138568 a(n) is the shortest substring containing all the permutations of {1,
               ...,n} as (not necessarily adjacent) substrings.
%C A138568 The strings a(n) of the sequence are the only strings that follow a particular 
               trend as shown by other string in the sequence. There are other strings 
               of the same length but the strings do follor the same pattern as 
               the one shown by all the strings in the sequence.
%D A138568 P.J. Koutas and T.C. Hu, Shortest String Containing All Permutations, 
               Discrete Mathematics, Vol. 11, 1975, pp. 125-132.
%H A138568 Hu, T.C. and Koutas, P.J., <a href="http://garden.irmacs.sfu.ca/?q=op/
               smallest_universal_supersequence">Shortest Substring</a>
%F A138568 a(n) = n..1..n..1..n (repeat n to 1 and 1 to n alternating for n number 
               of times)
%e A138568 a(4)= 4321234321234 because it contains all the permutations of the string 
               1234 as 1234 present in master string a(4) as 432123432(1234), 1243 
               as 432(12)3(43)21234, 1432 as 432(1)23(432)1234, 1423 as 432(1)23(4)3(2)12(3)4, 
               4321 as (4321)234321234 as so on and so forth.
%Y A138568 Cf. A136094.
%Y A138568 Sequence in context: A083962 A007942 A079794 this_sequence A092126 A085309 
               A092127
%Y A138568 Adjacent sequences: A138565 A138566 A138567 this_sequence A138569 A138570 
               A138571
%K A138568 nonn
%O A138568 1,2
%A A138568 Aniruddha Das (hi.annie.pal(AT)gmail.com), May 18 2008