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 three digits and A ≠ B. The first few such numbers are:

101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 454, 464, 474, 484, 494, ... (sequence A046075 in the OEIS)

For the full sequence of undulating numbers, see OEISA033619.

Some larger undulating numbers are: 1010, 80808, 171717, 989898989.

Properties

Undulating primes

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

2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 18181, 32323, 35353, 72727, 74747, 78787, 94949, 95959, ... (sequence A032758 in the OEIS)

References