A number is a mountain number in base    if its digits first increase and then decrease in that base, there is only one occurrence of the largest digit, and the first and last digits are 1.

For example, 1271, 123541, and 136797631 are all mountain numbers in base 10.

Here, I consider generalized mountain numbers in base 10, where the first and last digits may differ, as in 150, 27941, and 45678931. For brevity, I simply refer to them as mountain numbers. Note that, contrary to the OEIS entries linked below, I exclude single digit numbers.

In base    there are

mountain numbers. For base    the formula above gives a total of 173238 mountain numbers, from 120 to 123456789876543210. Among these, there are 7141 primes (from 131 to 134567897654321).

The first mountain numbers (in base 10) are 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181, 182, 183 more terms