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

Author

Neal Gersh Tolunsky, Jan 26 2025

Keywords

• nonn

Comments

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

Endpoints are included when comparing subsequences enclosed.

Examples

			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.
		

Links

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

Crossrefs

Cf. A363654, A380278, A380495.