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 20 such numbers are:
- 101, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 232, 242, 252, 262, 272, 282, 292, 303, 313 (sequence A046075 in OEIS)
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.
Famous quotes containing the words undulating and/or number:
“Truly man is a marvelously vain, diverse, and undulating object. It is hard to found any constant and uniform judgment on him.”
—Michel de Montaigne (1533–1592)
“He is the greatest artist who has embodied, in the sum of his works, the greatest number of the greatest ideas.”
—John Ruskin (1819–1900)