I am trying to figure out several sequences about simple numbers.
Given simple sequences following x^2 T times.
2^2(6 times) => 002 004 008 016 032 064
3^2(5 times) => 003 009 027 081 243
Then, I have to transform it into a sequence of sums of the previous numbers.
2 4 8 16 32 64
become 2 6 14 30 62 126
My question is: Given a sum of a sequence and the T(times), how to I figure out(GENERIC WAY) the x from x^2?
Example: Given 126
as the sum of the sequence, knowing it was interacted 6 times
, what is the x^2
6 times
in sequence, and then summed all the number, gives as result 126.
Answer: 2
.
Times:
1 2 3 4 5 6 7
Sequence 2^2
7 times:
2 4 8 16 32 64
Sum:
2 + 4 + 8 + 16 + 32 + 64 => 126