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

0,1

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

Table of n, a(n) for n=0..13.

Example

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

Crossrefs

Cf. A181391, A175100.

Sequence in context: A022428 A096186 A359817 * A352342 A298823 A219114

Adjacent sequences: A175038 A175039 A175040 * A175042 A175043 A175044

Keyword

nonn,more

Author

N. J. A. Sloane, Dec 02 2010

Status

approved