A145652 a(1)=1. a(n) = the largest integer such that the finite sequence (a(n-1),a(n-2),...a(n-a(n))) occurs somewhere as a subsequence in the finite sequence (a(1),a(2),...,a(n-1)).

1, 1, 2, 1, 3, 1, 3, 3, 2, 1, 2, 3, 5, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 2, 3

Offset

1,3

Comments

a(n+12) = a(n) for all n >= 14.

Links

Table of n, a(n) for n=1..105.

"Hagman", Sci Math Thread

Example

The subsequence of terms a(27) through a(29) in reversed order is (a(29),a(28),a(27)) = (3,3,2). This occurs in the first 29 terms of sequence A145652 like so: 1,1,2,1,3,1,(3,3,2),1,2,3,5,1,1,2,2,2,3,2,2,5,1,1,2,2,2,3,3. On the other hand, the subsequence of terms a(26) to a(29) in reversed order, (3,3,2,2) does not occur anywhere among the first 29 terms of sequence A145652. Since there are three terms in (3,3,2), then a(30) = 3.

Crossrefs

Sequence in context: A349918 A244797 A308659 * A368290 A111248 A100714

Adjacent sequences: A145649 A145650 A145651 * A145653 A145654 A145655

Keyword

nonn

Author

Leroy Quet, Oct 15 2008, corrected Oct 20 2008

Status

approved