  In 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.
