OFFSET
1,3
COMMENTS
The word 'set' means that every element is unique and order is irrelevant. {2,3}, for example, is equivalent to {3,2,2} and thus both could never appear in the sequence.
The pair of equal values a(n)=a(n+1) encloses the empty set {}, and thus after [a(1), a(2)] = [1, 1] no two equal values will occur one after the other.
A new value is always followed by 1.
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program
EXAMPLE
a(2)=1, establishing the empty set, [1,1] -> {}.
a(4)=1, creating the set [1,2,1] -> {2}, which is distinct from any set enclosed by consecutive equal values that has appeared thus far.
a(8)=2. a(8) cannot be 1 since this would again create the empty set enclosed already by [a(1), a(2)] = [1, 1]. 2 creates the set [2,3,1,2] = {1,3} which is distinct from any other set thus far.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Jan 19 2024
EXTENSIONS
More terms from Rémy Sigrist, Jan 20 2024
STATUS
approved