The four-antipalindrome conjecture
An antipalindrome is a natural number whose canonical base- expansion equals the complement of its reversal. The claim concerns all even natural numbers.
Four-antipalindrome conjecture. Every even natural number is the sum of at most antipalindromes.
The source says that the conditional bound of is probably far from optimal and that numerical evidence supports this stronger bound. No proof is given, so the conjecture remains open.
References
Primary source
Aayush Rajasekaran, Jeffrey Shallit and Tim Smith, “Sums of Palindromes: an Approach via Automata”, arXiv:1706.10206 (2017).
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