In the sequence 1, 0, 1, 0, 1, 0, 3, 5... each member after the sixth one equals the units' digit of the sum of the six preceding numbers of the sequence.
Prove that the subsequence 0, 1, 0, 1, 0, 1, will never occur.
It's obvious there must exist a cycle, and that it must be at most 1,000,000 "steps" long... it was good that this problem required only a 1456-step long cycle!
Brute force and luck
