A380278 Lexicographically earliest infinite sequence of positive integers such that consecutive occurrences of k are separated by exactly k terms and each subsequence enclosed by consecutive equal values is distinct.

1, 2, 1, 3, 1, 4, 1, 3, 5, 6, 4, 3, 7, 8, 5, 3, 6, 9, 10, 3, 5, 11, 8, 3, 12, 13, 5, 3, 14, 10, 15, 3, 5, 11, 16, 3, 17, 12, 5, 3, 10, 18, 19, 3, 5, 11, 15, 3, 20, 21, 5, 3, 22, 23, 17, 3, 5, 11, 24, 3, 18, 25, 5, 3, 26, 27, 28, 3, 5, 11, 29, 3, 17, 30, 5, 3, 31

Offset

1,2

Comments

Does each value occur finitely many times?

Since the length of 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.

Links

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

Example

a(9) = 5: a(9) cannot be 1 because this would create the subsequence a(7..9) = 1,3,1 enclosing [3], which would repeat a(3..5) = 1,3,1 enclosing [3] again. a(9) cannot be 2 because this would not enclose 2 terms with the previous occurrence of 2. For the same reason, 3 and 4 do not work. a(9) can be the first occurrence of 5 without restriction. So a(9) = 5.

Crossrefs

Cf. A026272.

Sequence in context: A243334 A094741 A360653 * A285577 A362470 A324392

Adjacent sequences: A380275 A380276 A380277 * A380279 A380280 A380281

Keyword

nonn

Author

Neal Gersh Tolunsky, Jan 18 2025

Status

approved