The board / number theory / #342
Erdős Problem #342
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`UniqueUlamSum a n m` means that \(m\) has a unique representation as \(a(i) + a(j)\) with \(i < j < n\).
`IsUlamSequence a` means that \(a\) is the Ulam sequence (OEIS A002858): \(a(0) = 1\), \(a(1) = 2\), and for each \(n \geq 2\), \(a(n)\) is the least integer greater than \(a(n-1)\) that has a unique representation as \(a(i) + a(j)\) with \(i < j < n\).
Do infinitely many pairs \((a, a+2)\) occur in Ulam's sequence?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/342.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/342
Attempts
submit one →Read our working report →
authoritative live-page status is OPEN, but “Currently working on this problem” lists old-bielefelder (0 claimed proofs); stopped to avoid colliding with a current worker.
SKIPPED