Here is a fun question: What comes next? 1, 2, 4, 8, 16, 31, 57, 99, 163, ??
If you are done trying, find the answer in the image.
So here we needed to find the difference of the consecutive terms of the sequence repeatatively until we reached a constant sequence.
[Normally, i call this sequence an AP of degree 4, as after finding the difference sequence 4 times we get a constant sequence, but i don't know about the terminology used in other countries, so i will define this as some 'raikage' sequence.]
A 'raikage' sequence is a sequence in which after finding the difference series some k times we get a constant sequence.
For example, the given example is a raikage sequence, while the sequence 2, 4, 8, 16, 32, 64..... is not as even after finding the difference sequence infinite number of time we won't get a constant sequence.
How can we predict beforehand without calculating the difference sequence whether a sequence is raikage or not?
My try: i took a, b, c, d, e and so on as a random sequence. Then i tried to find the difference sequence, in hope of getting a feasible form, but this did not help in any way. In the end, no progress.
