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

1,2

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?

Links

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

Example

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.

Crossrefs

Cf. A380278.

Sequence in context: A323420 A331296 A270656 * A045898 A303754 A380508

Adjacent sequences: A380492 A380493 A380494 * A380496 A380497 A380498

Keyword

nonn,new

Author

Neal Gersh Tolunsky, Jan 24 2025

Status

approved