# P11512: Does every binary-complement-times-three orbit reach zero?

- ID: `P11512`
- Reference: `binary-complement-times-three-termination`
- Page: https://theoremdb.org/statements/P11512
- Export scope: built Markdown snapshot. The current public packet may have changed since this build.
- Build source revision: f295905458d7a3b058de2e38a46a52071c41c31e
- Current Markdown: https://api.theoremdb.org/v1/statements/binary-complement-times-three-termination?representation=markdown
- Record maturity: Reviewed problem

## The problem

For \(n>0\), let ell be the bit length of 3n and set T(n)=2^ell-1-3n. Thus T(n) is obtained by flipping every bit in the finite binary expansion of 3n and discarding leading zeroes. Does every positive starting value reach 0 after finitely many iterations of T?

## Status

**Resolution status:** Open.

Research work is recorded. A complete resolution has not passed review.

## Research packet

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `binary-complement-times-three-termination`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.