def seq_diff(list_of_nums):
orig_list = list_of_nums
j = 0
while len(set(list_of_nums)) != 1:
lis = []
for i in range(len(list_of_nums)):
try:
lis.append(abs(list_of_nums[i]list_of_nums[i+1]))
except:
lis.append(abs(list_of_nums[i]list_of_nums[0]))
list_of_nums = lis
j = j+1
return orig_list, j
Sequence of Differences in Python
Carvia Tech  September 15, 2019  2 min read  3 views  Python Coding Problems
Given a set of four numbers representing a “circular array” we can test to see if the absolute values of the differences between each adjoining element will eventually coalesce into a single value.
For example, consider the set of four numbers: {1, 10, 8, 3}
.
We can repeatedly take the absolute values of the differences of the adjoining numbers. Since this is a circular array, calculate the value of the last element in the new array as the last number minus the first number.
For example, starting with {1, 10, 8, 3}

The first iteration will produce {9, 2, 5, 2} calculated as 1  10, 10  8, 8  3, 3  1.

The second iteration will produce {7, 3, 3, 7} calculated as 9  2, 2  5, 5  2, 2  9.

The third iteration will produce {4, 0, 4, 0} calculated as 7  3, 3 – 3, 3  7, 7 – 7.

The fourth iteration will produce {4, 4, 4, 4} calculated as 4  0, 0  4, 4  0, 0  4.
Input  Output 

1 0 0 0 
3 iterations were required for 1 0 0 0 
0 1 4 11 
5 iterations were required for 0 1 4 11 
0 0 0 2 
3 iterations were required for 0 0 0 2 
34 12 19 28 
4 iterations were required for 34 12 19 28 
100 200 321 345 
4 iterations were required for 100 200 321 345 
print(seq_diff([9934, 8543, 812, 1001]))
([9934, 8543, 812, 1001], 3)
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