A380508 Lexicographically earliest sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) distinct terms and each subsequence enclosed by consecutive equal values is distinct.

1, 2, 1, 3, 1, 2, 4, 5, 2, 5, 6, 2, 4, 6, 2, 7, 4, 2, 8, 9, 2, 4, 7, 2, 10, 4, 2, 8, 7, 2, 4, 11, 2, 10, 4, 7, 8, 12, 4, 11, 7, 10, 4, 8, 13, 7, 4, 14, 10, 8, 4, 7, 11, 15, 4, 10, 7, 8, 4, 14, 11, 7, 4, 10, 8, 16, 4, 7, 14, 10, 4, 8, 7, 11, 4, 17, 10, 7, 4, 8, 14

Offset

1,2

Comments

Endpoints are excluded when counting the number of distinct terms enclosed.

Endpoints are included when comparing subsequences enclosed.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Example

a(2) = 2, so 2's enclose 2 distinct terms. For example: a(2..6) = 2,1,3,1,2 enclosing the two distinct values in 1,3,1.
a(3) = 1, so 3's enclose 1 distinct term. In this case, there are no subsequences enclosed by a pair of 3s.
a(7) = 4: a(7) cannot be 1 as this would repeat the subsequence [1,2,1], which was seen before at a(1..3). 2 and 3 would not enclose a(2) = 2 and a(3) = 1 distinct terms respectively. So a(7) = 4, which has not occurred thus far.

Crossrefs

Cf. A363654, A380278, A380495.

Sequence in context: A380495 A045898 A303754 * A257918 A257912 A036262

Adjacent sequences: A380505 A380506 A380507 * A380509 A380510 A380511

Keyword

nonn

Author

Neal Gersh Tolunsky, Jan 26 2025

Status

approved