{"id":"palomar/PALOMAR-2026-10-27-000006","url":"https://github.com/dvgyl/oeis-proofs/tree/55ad2bd4804b6bcefeeb6c21eb06eac8b09c45d8/lean","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-27-000006-v1.json","repo":"https://github.com/dvgyl/oeis-proofs","tags":["math.NT","math.CO","msc:11B50","msc:05A15","msc:13F25","msc:11B83","msc:68V15"],"score":0,"title":"Proofs and corrections of OEIS conjectures","trust":"high","domain":"math.NT","source":"palomar","authors":["Dev D. Goyal"],"reviews":0,"subject":"math.NT","summary":"Machine-checked proofs of conjectures recorded in 29 entries of the On-Line Encyclopedia of Integer Sequences (OEIS), together with corrections of the four conjectured statements that turn out to be false. Most of the sequences are coefficients of formal power series defined by functional equations, and most of the results describe their residues modulo small integers. The results form six families and a group of further results: the equation A(x*A - m*x*A^2) = x^2 (parity, residues modulo m^2, binary-digit divisibility and prime exponents for every m, with corrected residue classifications…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-27","reactions":{},"formalized":true}