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

2, 4, 9, 12, 15, 19, 24, 28, 33, 41, 45, 49, 54, 61

Offset: 0

Author

N. J. A. Sloane, Dec 02 2010

Keywords

• nonn
• more

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.

Examples

			d  length  lex-min seq
0   2      0 0
1   4      0 0 1 0
2   9      0 0 1 0 2 0 2 2 1
3  12      1 0 0 1 3 0 3 2 0 3 3 1
4  15      0 2 3 0 3 2 4 0 4 2 4 2 2 1 0
5  19      0 1 3 5 4 0 5 3 5 2 0 5 3 5 2 5 2 2 1
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
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
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
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
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
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
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
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
		

References

• Email from David Applegate, Oct 19 2010

Crossrefs

Cf. A181391, A175100.