A378381 - OEIS

A378381

Lexicographically earliest sequence such that each set of terms enclosed by two equal values, including the endpoints, contains a distinct number of elements.

1, 1, 2, 3, 2, 4, 3, 5, 6, 4, 7, 3, 8, 9, 5, 10, 6, 11, 12, 7, 13, 3, 14, 15, 16, 8, 17, 9, 18, 5, 19, 20, 10, 21, 6, 22, 23, 11, 24, 12, 25, 26, 13, 27, 3, 28, 29, 30, 31, 14, 32, 15, 33, 16, 34, 8, 35, 36, 17, 37, 9, 38, 39, 18, 40, 5, 41, 42, 43, 19, 44, 20, 45

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OFFSET

1,3

COMMENTS

The word 'set' means that every element is unique. For example, the set {1,1,2} contains 2 elements (not 3).

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

Two consecutive values enclose 1 term, and thus after [a(1), a(2)] = [1, 1], no consecutive equal values occur again.

LINKS

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

EXAMPLE

a(4) cannot be 1 since this would create a second pair enclosing two values, [1,2,1] being an equivalent set to [1,2,1,1]. We cannot have a(4)=2 because [1,2,1] would enclose the same number of elements as [2,1,2]. So a(4)=3, which has not occurred before.

PROG

(Python)

from itertools import islice

def agen(): # generator of terms

e, a = set(), []

while True:

an, allnew = 0, False

while not allnew:

allnew, an, ndset = True, an+1, set()

for i in range(len(a)):

if an == a[i]:

nd = len(set(a[i:]))