{"schema":"vela.problem-packet.v0.1","problem":340,"statement":"Let $A=\\{1,2,4,8,13,21,31,45,66,81,97,\\ldots\\}$ be the greedy Sidon sequence: we begin with $1$ and iteratively include the next smallest integer that preserves the Sidon property (i.e. there are no non-trivial solutions to $a+b=c+d$). What is the order of growth of $A$? Is it true that\\[\\lvert A\\cap \\{1,\\ldots,N\\}\\rvert \\gg N^{1/2-\\epsilon}\\]for all $\\epsilon>0$ and large $N$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_151d682861664f8f","kind":"dead_end","claim":"attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A005282","name":"Mian-Chowla sequence (a B_2 sequence): a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all distinct.","terms":"1,2,4,8,13,21,31,45,66,81,97,123,148,182,204,252,290,361,401,475,565,593,662,775,822,916,970,1016,1159,1312,1395,1523,15","url":"https://oeis.org/A005282"},{"id":"A080200","name":"Numbers that do not occur as differences between terms of the Mian-Chowla sequence A005282.","terms":"33,88,98,99,105,106,112,126,130,132,134,150,152,154,156,162,163,165,170,176,184,188,198,205,214,215,217,220,222,228,234,","url":"https://oeis.org/A080200"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}