A number is undulating in base    if it has at least 3 digits and it is made of exactly two distict digits which alternate, like 252 or 373737 in base 10 or 21=(10101)₂.

David Moews has proved that there are only 4 undulating squares, namely 121, 484, 676, and 69696.

The first numbers which are undulating in at least 2 bases b <= 16 are 10, 46, 50, 55, 67, 78, 85, 92, 98, 100, 104, 109, 119, 121, 130, 135, 136, 141, 145, 151, 154, 164, 166, 170, 178, 181, 182, 185, 191, 197, 200

Below, the spiral pattern of undulating numbers up to  . See the page on prime numbers for an explanation and links to similar pictures.

The first undulating numbers in base 10 are 101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 232, 242, 252, 262, 272, 282, 292, 303, 313 more terms