Open problem

FPRD-C04

Existence of a decimal Lychrel number

Exact statement

Does there exist a positive decimal integer whose reverse-and-add orbit never reaches a palindrome? In particular, does the orbit of 196196 avoid palindromes forever?

StatusOpen; no FPRD resolution
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

196 is the smallest familiar decimal candidate, but the public sources checked for this ingestion continue to describe the decimal problem as unproved.

Proof or evidence

The cited FPRD sources contain bounded experiments and exact one-step structure only. OEIS A023108 labels its terms as apparent candidates, and p196.org documents computation and carry observations rather than a proof.

Verification notes

The statement is presented as an open problem and separated from every finite observation on this page.

Limitations

  • No claim is made that 196 is a Lychrel number.
  • No novelty or external review is claimed for the FPRD observations.

Open work

Pursue finite structural results and exact interfaces without treating bounded orbit searches or random-like statistics as an infinite proof.