Weighted support criteria for reciprocal Mersenne subseries
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…
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