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danbruc a day ago

Combining two consecutive integers starting with an even one yields one.

  xxxxxxx0 ^ xxxxxxx1 = 00000001 
If we start at a number divisible by four and do this twice, we get one twice.

  xxxxxx00 ^ xxxxxx01 = 00000001
  xxxxxx10 ^ xxxxxx11 = 00000001
And combining the two of course yields zero and we are right back at the start.