A175100 - OEIS

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A175100

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

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	`Table of n, a(n) for n=2..14.`
	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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Last modified May 19 10:40 EDT 2013. Contains 225429 sequences.