A380495 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by k distinct values and each subsequence enclosed by consecutive equal values is distinct.

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

Offset: 1

Author

Neal Gersh Tolunsky, Jan 24 2025

Keywords

• nonn

Comments

Since the number of distinct terms in a subsequence is given by its enclosing values, the sequence remains the same whether we include those endpoints or not when checking the uniqueness of subsequences.

Without the condition that subsequences enclosed by consecutive equal values are distinct, this sequence would be A001511 (the ruler function).

Does each value occur finitely many times?

Examples

			a(7)=4: a(7) cannot be 1 because this would make a(5..7) a repeat of a(1..3) = 1,2,1. a(7) cannot be 2 or 3 as these would not enclose 2 or 3 distinct terms respectively. So a(7) must be 4.
		

Links

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

Crossrefs

Cf. A380278.