The sequence 1, 31, 331, 3331, 33331, ... (OEIS A033175) consisting of , 1, ... 3s followed by a 1 has its
th term is given by

The result is prime for ,
2, 3, 4, 5, 6, 7, 17, 39, ... (OEIS A055520);
i.e., for 31, 331, 3331, 33331, 333331, 3333331, 33333331, ... (OEIS A051200),
a fact which Gardner (1997) calls "a remarkable pattern that is entirely accidental
and leads nowhere."