A366493 - OEIS

%I #20 Dec 07 2024 02:03:04

%S 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,

%T 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,

%U 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

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

%C A new value is always followed by 1.

%H Samuel Harkness, <a href="/A366493/b366493.txt">Table of n, a(n) for n = 1..10000</a>

%H Samuel Harkness, <a href="/A366493/a366493.m.txt">MATLAB program</a>

%e a(2)=1 because the subsequence (1,1) has not occurred before.

%e 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

%o (MATLAB) See Links section.

%o (Python)

%o from itertools import islice

%o def agen(): # generator of terms

%o     m, a = set(), []

%o     while True:

%o         an, allnew = 0, False

%o         while not allnew:

%o             allnew, an, mn = True, an+1, set()

%o             for i in range(len(a)):

%o                 if an == a[i]:

%o                     t = tuple(a[i:]+[an])

%o                     if t in m or t in mn: allnew = False; break

%o                     mn.add(t)

%o         yield an; a.append(an); m |= mn

%o print(list(islice(agen(), 111))) # _Michael S. Branicky_, Dec 06 2024

%Y Cf. A330896.

%K nonn,easy

%O 1,3

%A _Neal Gersh Tolunsky_, Oct 10 2023