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Search: id:A138568
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| A138568 |
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a(n) is the shortest substring containing all the permutations of {1,...,n} as (not necessarily adjacent) substrings. |
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1
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| 1, 212, 3212321, 4321234321234, 543212345432123454321, 6543212345654321234565432123456, 7654321234567654321234567654321234567654321
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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P.J. Koutas and T.C. Hu, Shortest String Containing All Permutations, Discrete Mathematics, Vol. 11, 1975, pp. 125-132.
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LINKS
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Hu, T.C. and Koutas, P.J., Shortest Substring
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FORMULA
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a(n) = n..1..n..1..n (repeat n to 1 and 1 to n alternating for n number of times)
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EXAMPLE
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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.
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CROSSREFS
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Cf. A136094.
Sequence in context: A083962 A007942 A079794 this_sequence A092126 A085309 A092127
Adjacent sequences: A138565 A138566 A138567 this_sequence A138569 A138570 A138571
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KEYWORD
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nonn
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AUTHOR
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Aniruddha Das (hi.annie.pal(AT)gmail.com), May 18 2008
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