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

1,3

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).

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..7522

Neal Gersh Tolunsky, Ordinal transform of 7522 terms

Example

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.

Prog

(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

Crossrefs

Cf. A366625.

Sequence in context: A105258 A329173 A366493 * A352998 A339351 A284322

Adjacent sequences: A378773 A378774 A378775 * A378777 A378778 A378779

Keyword

nonn

Author

Neal Gersh Tolunsky, Dec 06 2024

Status

approved