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

Author

Neal Gersh Tolunsky, Oct 10 2023

Keywords

• nonn
• easy

Comments

A new value is always followed by 1.

Examples

			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
		

Links

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

Crossrefs

Cf. A330896.

Programs

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