Open Research Index

Cubic-rate irrationality for reciprocal sums

Will Cook

Palomar Registrypalomar/PALOMAR-2026-10-22-000036Oct 22, 2026math.NTscore 0

Every positive strictly increasing zero-indexed integer sequence a with n^3(a_n^2/a_(n+1) - 1 - 3/n) tending to zero has an irrational reciprocal sum. The entry also states the exact integer-tail and number-field steps used to exclude the resulting cubic profile: positive-density exceptions, primitive gcd reduction, square specialisation, scale twelve, forbidden words modulo seven, and regular-rate extraction. The printed one-indexed paper theorem uses its stated finite-prefix argument. The separate bounded-increment Sylvester criterion in the paper is outside this configuration, and the…

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