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 A175100 Length of longest A181391-suffix other than 11...1 with entries (1 <= a(n) <= d). 3
 5, 7, 11, 13, 16, 22, 23, 35, 35, 35, 36, 43, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS A sequence is an "A181391-suffix" if it satisfies the following definition which is less stringent than that of A181391. For n>=1, if there exists an m < n such that a(m) = a(n), take the largest such m and set a(n+1) = n-m; otherwise set a(n+1) either to 0 or to a number >= n. The motivation for calling this an "A181391-suffix" is that we treat n <= 0 as a kind of unknown prefix - each entry has to be consistent with some prefix, but we don't require the same prefix for all values. This sequence arises when searching for possible cycles in sequences generated by the rule in A181391. For example, 1 2 2 1 3 5 is an A181391-suffix, since the sample prefixes below justify the *'d entries: ....0.0.|.1*.2.2.1.3.5 ....1.x.|.1.2*.2.1.3.5 ......2.|.1.2.2*.1.3.5 ......3.|.1.2.2.1.3.5* Clearly, any continuation, including any cycle, from any starting point is an A181391-suffix. REFERENCES Email from David Applegate, Oct 19 2010 LINKS EXAMPLE d  length  lex-min seq 2   5      2 1 2 2 1 3   7      1 3 2 3 2 2 1 6 4  11      1 4 2 3 4 3 2 4 3 3 1 10 5  13      3 1 3 2 5 5 1 5 2 5 2 2 1 6 6  16      3 1 2 6 5 5 1 5 2 6 6 1 5 5 1 3 15 7  22      1 7 2 5 6 7 4 7 2 6 5 7 4 6 4 2 7 5 7 2 4 6 8 8  23      1 7 2 5 6 7 4 7 2 6 5 7 4 6 4 2 7 5 7 2 4 6 8 0 9  35      2 1 7 5 6 9 8 7 5 5 1 9 6 8 7 7 1 6 5 9 8 7 6 5 5 1 9 7 6 6 1 5 7 5 2 34 10  35      2 1 7 5 6 9 8 7 5 5 1 9 6 8 7 7 1 6 5 9 8 7 6 5 5 1 9 7 6 6 1 5 7 5 2 34 11  35      2 1 7 5 6 9 8 7 5 5 1 9 6 8 7 7 1 6 5 9 8 7 6 5 5 1 9 7 6 6 1 5 7 5 2 34 12  36      3 3 1 5 4 12 6 11 8 11 2 12 6 6 1 12 4 12 2 8 11 11 1 8 4 8 2 8 2 2 1 8 4 8 2 5 32 13  43      12 6 2 8 5 13 6 5 3 11 12 10 12 2 11 5 8 13 12 6 13 3 13 2 10 13 3 5 12 10 5 3 5 2 10 5 3 5 2 5 2 2 1 0 14  43      11 14 9 8 9 2 12 7 11 8 6 12 5 13 14 13 2 11 9 14 5 8 12 11 6 14 6 2 11 5 9 12 9 2 6 8 14 11 9 6 5 11 4 0 CROSSREFS Cf. A181391, A175041. Sequence in context: A113837 A196276 A079498 * A035035 A113909 A111906 Adjacent sequences:  A175097 A175098 A175099 * A175101 A175102 A175103 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Dec 02 2010 STATUS approved

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