OFFSET
1,2
COMMENTS
The sequence S starts with a(1) = 1 and a(2) = 9. S is extended by duplicating the first term A among the not yet duplicated terms of S, under the condition that the sum [a(n-1) + a(n)] is a palindrome. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the sum [a(n-1) + a(n)] is not a palindrome. 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) = 9
Can we duplicate a(1) to form a(3)? No, as a(2) + a(3) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(2) + X] is not a palindrome. We get a(3) = 3.
Can we duplicate a(1) to form a(4)? Yes, as a(3) + a(4) = 4, which is a palindrome. We get a(4) = 1.
Can we duplicate a(2) to form a(5)? No, as a(4) + a(5) would be 10 and 10 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(4) + X] is not a palindrome; we get a(5) = 11.
Can we duplicate a(2) to form a(6)? No, as a(5) + a(6) would be 20 and 20 is not a palindrome. We thus extend S with the smallest integer X not yet in S such that [a(5) + X] is not a palindrome; we get a(6) = 2.
Can we duplicate a(2) to form a(7)? Yes, as [a(6) + a(7)] = 11, which is a palindrome. We get a(7) = 9.
Etc.
CROSSREFS
KEYWORD
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Mar 11 2019
STATUS
approved