2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160968In his July 1974 Scientific American column, Martin Gardner mentioned the Handbook of Integer Sequences, which then contained 2372 sequences. Today the On-Line Encyclopedia of Integer Sequences (the OEIS) contains 140000 sequences. This paper discusses eight of them, suggested by the theme of the Eighth Gathering For Gardner: they are all infinite, and all 'ateful in one way or another. Each one is connected with an unsolved problem. The sequences are related to: hateful numbers, Angelini's 1995 puzzle, the persistence of a number, Alekseyev's 123 sequence, the curling number conjecture, Quet's prime-generating recurrence, the traveling salesman's problem, and the Riemann Hypothesis.5 pages; paper for 8th Gathering for [Martin] GardnerCombinatoricsNumber Theory10A05, 10A35, 10L10, 10L99, 11M26, 90C27text