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:
“Who among us has not, in moments of ambition, dreamt of the miracle of a form of poetic prose, musical but without rhythm and rhyme, both supple and staccato enough to adapt itself to the lyrical movements of our souls, the undulating movements of our reveries, and the convulsive movements of our consciences? This obsessive ideal springs above all from frequent contact with enormous cities, from the junction of their innumerable connections.”
—Charles Baudelaire (1821–1867)
“How often should a woman be pregnant? Continually, or hardly ever? Or must there be a certain number of pregnancy anniversaries established by fashion? What do you, at the age of forty-three, have to say on the subject? Is it a fact that the laws of nature, or of the country, or of propriety, have ordained this time of life for sterility?”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)