cp's OEIS Frontend

A175100 Length of longest A181391-suffix other than 11...1 with entries (1 <= a(n) <= d).

%I A175100 #11 Mar 30 2012 17:21:03
%S A175100 5,7,11,13,16,22,23,35,35,35,36,43,43
%N A175100 Length of longest A181391-suffix other than 11...1 with entries (1 <= a(n) <= d).
%C A175100 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.
%C A175100 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.
%C A175100 This sequence arises when searching for possible cycles in sequences generated by the rule in A181391.
%C A175100 For example, 1 2 2 1 3 5 is an A181391-suffix, since the sample prefixes below justify the *'d entries:
%C A175100 ....0.0.|.1*.2.2.1.3.5
%C A175100 ....1.x.|.1.2*.2.1.3.5
%C A175100 ......2.|.1.2.2*.1.3.5
%C A175100 ......3.|.1.2.2.1.3.5*
%C A175100 Clearly, any continuation, including any cycle, from any starting point is an A181391-suffix.
%D A175100 Email from _David Applegate_, Oct 19 2010
%e A175100 d  length  lex-min seq
%e A175100 2   5      2 1 2 2 1
%e A175100 3   7      1 3 2 3 2 2 1 6
%e A175100 4  11      1 4 2 3 4 3 2 4 3 3 1 10
%e A175100 5  13      3 1 3 2 5 5 1 5 2 5 2 2 1 6
%e A175100 6  16      3 1 2 6 5 5 1 5 2 6 6 1 5 5 1 3 15
%e A175100 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
%e A175100 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
%e A175100 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
%e A175100 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
%e A175100 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
%e A175100 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
%e A175100 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
%e A175100 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
%Y A175100 Cf. A181391, A175041.
%K A175100 nonn,more
%O A175100 2,1
%A A175100 _N. J. A. Sloane_, Dec 02 2010