The initial sequence is 1, 3, 7, 12, 18, 26, 35, etc. The difference between each term in that sequence produces a second sequence: 2, 4, 5, 6, 8, 9, 10, etc. If you merge those two sequences together in sorted order, you get 1, 2, 3, 4, 5, 6, 7, etc. Each whole number appears in the result exactly once.
By end of the sequence shown on the page, the contiguous part has only reached 61. After that it's full of gaps: it's hit 1689, but has not yet hit 62. The last three differences shown there are 59, 60, 61. So it will list all integers mainly because the differences are increasing similar to the ordinary number line.
