cp's OEIS Frontend

A175041 Length of longest A181391-suffix other than 11...1 with entries (0 <= a(n) <= d).

%I A175041 #10 Mar 30 2012 17:21:03
%S A175041 2,4,9,12,15,19,24,28,33,41,45,49,54,61
%N A175041 Length of longest A181391-suffix other than 11...1 with entries (0 <= a(n) <= d).
%C A175041 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 A175041 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 A175041 This sequence arises when searching for possible cycles in sequences generated by the rule in A181391.
%C A175041 For example, 1 2 2 1 3 5 is an A181391-suffix, since the sample prefixes below justify the *'d entries:
%C A175041 ....0.0.|.1*.2.2.1.3.5
%C A175041 ....1.x.|.1.2*.2.1.3.5
%C A175041 ......2.|.1.2.2*.1.3.5
%C A175041 ......3.|.1.2.2.1.3.5*
%C A175041 Clearly, any continuation, including any cycle, from any starting point, is an A181391-suffix.
%D A175041 Email from _David Applegate_, Oct 19 2010
%e A175041 d  length  lex-min seq
%e A175041 0   2      0 0
%e A175041 1   4      0 0 1 0
%e A175041 2   9      0 0 1 0 2 0 2 2 1
%e A175041 3  12      1 0 0 1 3 0 3 2 0 3 3 1
%e A175041 4  15      0 2 3 0 3 2 4 0 4 2 4 2 2 1 0
%e A175041 5  19      0 1 3 5 4 0 5 3 5 2 0 5 3 5 2 5 2 2 1
%e A175041 6  24      2 1 0 3 0 2 5 0 3 5 3 2 6 0 6 2 4 0 4 2 4 2 2 1
%e A175041 7  28      0 0 1 0 2 7 0 3 0 2 5 0 3 5 3 2 6 0 6 2 4 0 4 2 4 2 2 1
%e A175041 8  33      3 7 2 5 6 7 4 7 2 6 5 7 4 6 4 2 7 5 7 2 4 6 8 0 0 1 0 2 8 6 8 2 4
%e A175041 9  41      2 0 2 2 1 5 0 5 2 5 2 2 1 8 0 8 2 5 8 3 0 6 0 2 7 0 3 7 3 2 6 9 0 7 6 4 0 4 2 9 8
%e A175041 10 45      9 5 0 7 6 6 1 0 5 7 6 5 3 0 6 4 0 3 5 7 10 0 5 4 8 0 4 3 10 8 5 8 2 0 8 3 8 2 5 8 3 5 3 2 6
%e A175041 11 49      7 4 6 7 3 5 0 7 4 7 2 11 0 6 11 3 11 2 7 9 0 8 0 2 6 11 9 7 9 2 6 6 1 0 11 9 7 9 2 9 2 2 1 10 0 11 11 1 5
%e A175041 12 54      7 4 6 7 3 12 0 7 4 7 2 11 0 6 11 3 11 2 7 9 0 8 0 2 6 11 9 7 9 2 6 6 1 0 11 9 7 9 2 9 2 2 1 10 0 11 11 1 5 0 5 2 10 9
%e A175041 13 61      4 5 2 0 12 5 4 6 10 12 5 5 1 0 10 6 8 0 4 12 10 6 6 1 11 0 8 10 7 0 4 12 12 1 10 7 7 1 4 8 13 0 12 10 9 0 4 8 8 1 12 8 3 0 8 3 3 1 8 4 13
%Y A175041 Cf. A181391, A175100.
%K A175041 nonn,more
%O A175041 0,1
%A A175041 _N. J. A. Sloane_, Dec 02 2010