OFFSET
1,2
COMMENTS
The sequence S starts with a(1) = 1 and a(2) = 2. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that the absolute difference |a(n-1) - a(n)| is prime. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the absolute difference |a(n-1) - a(n)| is not prime. S is the lexicographically earliest sequence with this property.
LINKS
Jean-Marc Falcoz, Table of n, a(n) for n = 1..10002
EXAMPLE
S starts with a(1) = 1 and a(2) = 2
Can we duplicate a(1) to form a(3)? No, as |a(2) - a(3)| would be 1 and 1 is not prime. We thus extend S with the smallest integer X not yet in S such that |a(2) - X| is not prime. We get a(3) = 3.
Can we duplicate a(1) to form a(4)? Yes, as |a(3) - a(4)| = 2, which is prime. We get a(4) = 1.
Can we duplicate a(2) to form a(5)? No, as |a(4) - a(5)| would be 1 and 1 is not prime. We thus extend S with the smallest integer X not yet in S such that |a(4) - X| is not prime; we get a(5) = 5.
Can we duplicate a(2) to form a(6)? Yes, as |a(6) - a(5)| = 3, which is prime; we get a(6) = 2.
Etc.
CROSSREFS
KEYWORD
AUTHOR
Alexandre Wajnberg and Eric Angelini, Mar 11 2019
STATUS
approved