I’ve discovered this interesting way of making sequences. Start off with any three numbers, then any subsequent number is the sum of the previous number and the number before that, minus the number before that.
In mathematical terms a(n) = a(n-1)+a(n-2)-a(n-3)
If you start with, say, 1, 1, 1, the sequence continues with 1s forever.
If you start with 1, 2, 3, the sequence continues to count up through all of the integers in turn.
I plugged in some random numbers as the first three terms and looked way down the list that was produced:
The 243rd number in the sequence is 1092.
The 302nd number in the sequence is 1355.
The 577th number in the sequence is 2595.
What were the first three numbers in the sequence?