This is a visualization of Recamán's sequence named after Colombian mathematician Bernardo Recamán.
a(0) = 0 For n > 0, a(n) = a(n-1) - n (if positive and not already in the sequence) otherwise a(n) = a(n-1) + n
The first 10 numbers are as follows: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21.
Starting from 0, the first question is as follows: Can I subtract 1? I cannot, as one of the rules of the sequence is that the numbers have to be positive. Hence, the next number in the sequence is 1. Can I then subtract 2? No, because 0 is already in the sequence. The same holds true for 3. So far, I could only use the second formula: 0 + 1 = 1; 1 + 2 = 3; 3 + 3 = 6. Can I now subtract 4? Yes indeed, because the resulting number 2 is not negative and not yet in the sequence. And so on and so forth.
Further infos can be found here: The Online Encyclopedia of Integer Sequences
You can check out my visualization here! (Ideally open in Chrome!!)