An undulating number is a number that has the digit form ababab... when in the base 10

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 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

101 (number)

101 is the natural number following 100 and preceding 102.It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one"...

, 121

121 (number)

121 is the natural number following 120 and preceding 122.-In mathematics:One hundred [and] twenty-one is a square and is the sum of three consecutive primes . There are no squares besides 121 known to be of the form 1 + p + p^2 + p^3 + p^4, where p is prime...

, 131

131 (number)

131 is the natural number following 130 and preceding 132.-In mathematics:131 is a Sophie Germain prime, the second 3-digit palindromic prime, and also a permutable prime with 113 and 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an Eisenstein prime...

, 141

141 (number)

141 is the natural number following 140 and preceding 142.-In mathematics:141 is a centered pentagonal number. It is the sum of the sums of divisors of the first thirteen integers....

, 151

151 (number)

151 is a natural number. It follows 150 and precedes 152.-In mathematics:151 is the 36th prime number, the previous is 149, with which it comprises a twin prime. 151 is also a palindromic prime. 151 is a centered decagonal number...

, 161

161 (number)

161 is an odd natural number between 160 and 162-In geography:* Bahrain and Brunei each have coastlines that are 161 kilometers in length.* Bhutan ranks #161 in world population...

, 171

171 (number)

171 is the natural number following 170 and preceding 172.-In mathematics:* 171 is an odd number* 171 is a composite number* 171 is a deficient number* 171 is a Harshad number, divisible by the sum of its digits...

, 181

181 (number)

181 is the natural number between 180 and 182.-In mathematics:* 181 is an odd number* 181 is a centered number** 181 is a centered pentagonal number** 181 is a centered 12-gonal number** 181 is a centered 18-gonal number...

, 191

191 (number)

191 is the natural number following 190 and preceding 192.-In mathematics:* 191 is an odd number* 191 is a centered 19-gonal number* 191 is a deficient number, as 1 is less than 191...

, 202

202 (number)

202 is the natural number following 201 and preceding 203. It may be written as "two hundred two" or "two hundred and two".-In mathematics:...

, 212

212 (number)

212 is the natural number following 211 and preceding 213.- In mathematics :* 22·53* totient sum for the first 26 integers* In Fahrenheit degrees, the boiling point of water at sea level- In other fields :...

, 232, 242

242 (number)

242 is the natural number following 241 and preceding 243.-In mathematics:242 is the smallest integer to start a run of four consecutive integers with the same number of divisors.242 is a nontotient since there is no integer with 242 coprimes below it....

, 252, 262, 272, 282, 292, 303, 313

313 (number)

313 is an integer following 312 and preceding 314. 313 is a:* prime number* twin prime with 311* centered square number* long prime* pythagorean prime* regular prime* palindromic prime in both decimal and binary.* truncatable prime* happy number...

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.