Undulating number

An undulating number is a number that has the digit form ababab... when in the base 10 number system. It is sometimes restricted to non-trivial undulating numbers which are required to have at least 3 digits and a ≠ b. The first few such numbers are:

For the full sequence of undulating numbers, see  .

Some higher undulating numbers are: 6363, 80808, 1717171.

For any n ≥ 3, there are 9 × 9 = 81 non-trivial n-digit undulating numbers, since the first digit can have 9 values (it cannot be 0), and the second digit can have 9 values when it must be different from the first.

An undulating prime is an undulating number that is also prime. In every base, all undulating primes having at least 3 digits have an odd number of digits. The undulating primes in base 10 are:

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