A380507 Lexicographically earliest infinite sequence of positive integers such that for any n, consecutive occurrences of n are separated by a(n) terms and each subsequence enclosed by consecutive equal values is distinct.

1, 2, 1, 3, 1, 3, 4, 3, 5, 3, 4, 6, 7, 8, 4, 6, 9, 7, 4, 6, 10, 11, 4, 6, 10, 12, 4, 6, 10, 13, 4, 6, 10, 14, 4, 6, 10, 13, 15, 6, 10, 16, 14, 6, 10, 13, 17, 6, 10, 18, 19, 6, 10, 13, 20, 6, 10, 18, 21, 6, 10, 13, 22, 6, 10, 18, 23, 6, 10, 13, 24, 6, 10, 18, 22

Offset: 1

Author

Neal Gersh Tolunsky, Jan 25 2025

Keywords

• nonn

Comments

Endpoints are included when comparing subsequences enclosed by consecutive equal values.

Examples

			a(1) = 1 means that consecutive 1s enclose 1 term. For example: a(1..3) = [1,2,1] encloses [2].
a(2) = 2 means that consecutive 2s have length 2. In this case, there are no subsequences enclosed by a pair of 2s.
a(3) = 1 means that consecutive 3s enclose 1 term. For example, a(3..5) = [3,1,3] encloses [1].
a(7) = 4: a(7) cannot be 1 as this would repeat the subsequence [1,3,1], which was seen before at a(3..5). 2 and 3 would not enclose a(2) = 2 and a(3) = 1 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.