A366493 Lexicographically earliest sequence such that each subsequence enclosed by two equal terms is distinct.

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

Offset

1,3

Comments

A new value is always followed by 1.

Links

Samuel Harkness, Table of n, a(n) for n = 1..10000

Samuel Harkness, MATLAB program

Example

a(2)=1 because the subsequence (1,1) has not occurred before.
a(8)=3 because every smaller number would form a subsequence that has occurred already. a(8) cannot be 1 because this would make the subsequence (1,1), which was seen before at i=1,2. a(8) cannot be 2 because then we would have the subsequence (2,1,2) for a second time (first at i=3-5): 1,1,2,1,2,2,1,2

Prog

(MATLAB) See Links section.
(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(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(), 111))) # Michael S. Branicky, Dec 06 2024

Crossrefs

Cf. A330896.

Sequence in context: A095686 A105258 A329173 * A378776 A352998 A339351

Adjacent sequences: A366490 A366491 A366492 * A366494 A366495 A366496

Keyword

nonn,easy

Author

Neal Gersh Tolunsky, Oct 10 2023

Status

approved