A378776 Lexicographically earliest sequence of positive integers such that each multiset enclosed by a pair of equal terms, including the endpoints, is distinct.

1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 3, 1, 2, 4, 1, 2, 3, 2, 3, 1, 3, 2, 4, 2, 1, 3, 3, 4, 1, 3, 4, 1, 4, 1, 2, 3, 4, 1, 2, 4, 4, 1, 2, 5, 1, 2, 3, 4, 2, 3, 4, 1, 5, 1, 2, 3, 4, 3, 1, 5, 2, 3, 1, 4, 5, 1, 3, 2, 4, 6, 1, 2, 3, 4, 5, 1, 2, 3, 5, 2, 1, 4, 5, 2, 1, 4, 6, 1

Offset: 1

Author

Neal Gersh Tolunsky, Dec 06 2024

Keywords

• nonn

Comments

Note that we are considering multisets between every pair of equal values, not just those that appear consecutively.

Each positive integer occurs infinitely many times.

A new value is always followed by 1.

First differs from A366493 at a(19).

Examples

			a(19) = 3: a(19) cannot be 1 because then a(15..19) = (1, 2, 3, 2, 1) would be the same multiset as a(6..10) = (2, 1, 3, 1, 2). a(19) cannot be 2 since this would make a(18-19) = (2,2), which is the same multiset as a(5-6). a(19) can be 3 since this does not create any repeat multiset.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..7522
• Neal Gersh Tolunsky, Ordinal transform of 7522 terms

Crossrefs

Cf. A366625.

Programs

Python

from itertools import islice
def agen(): # generator of terms
    m, a = set(), []
    while True:
        an, allnew = 0, False
        while not allnew:
            allnew, an, mn = True, an+1, set()
            for i in range(len(a)):
                if an == a[i]:
                    t = tuple(sorted(a[i:]+[an]))
                    if t in m or t in mn: allnew = False; break
                    mn.add(t)
        yield an; a.append(an); m |= mn
print(list(islice(agen(), 88))) # Michael S. Branicky, Dec 06 2024