It is easy to verify that up to    there are exactly    alternating numbers in base 10.

The first alternating numbers in base 10 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 101 more terms

Below, the spiral pattern of alternating numbers up to 6400. See the page on prime numbers for an explanation and links to similar pictures.

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many alternating numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.