{"id":"palomar/PALOMAR-2026-09-25-000009","url":"https://github.com/wcook04/plectis-erdos-lean/tree/b85ed30805188eb4390a686b111294b24363418e","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-25-000009-v1.json","repo":"https://github.com/wcook04/plectis-erdos-lean","tags":["math.NT","msc:11J72","msc:11B83","number-theory","irrationality","mersenne-numbers"],"score":0,"title":"Weighted support criteria for reciprocal Mersenne subseries","trust":"high","domain":"math.NT","source":"palomar","authors":["Will Cook"],"reviews":0,"subject":"math.NT","summary":"For an infinite set A of positive integers and an integer base b at least 2, consider the reciprocal Mersenne subseries X_A(b) = sum over a in A of 1/(b^a - 1). For a finite nonempty set P of primes, write h_P(a) for the P-part of a. The principal theorem proves irrationality when sum over a in A of h_P(a)/(a*(b^h_P(a) - 1)) converges. The base-two condition implies irrationality at every integer base at least 2 for every infinite subset of the host support. This is a sufficient support criterion, not a solution of the universal Erdős problem. It includes reciprocal-summable supports; the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true}