Question

3. The Hofstadter Conway sequence is defined by a(1)=a(2)=1 and (for n>2 by) a(n)=a(a(n-1))+a(n-a(n-1)). Write a function to quickly compute this sequence.

>>> [hc(i) for i in range(1,20)]
[1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 10, 11]

Answer 1

The programming language used is Python 3.8.

The function name is hc() which takes in the parameter value n.

The code snippet of the function is:

def hc(n): 
    List = [0, 1, 1] 
    if n<= 0:
      return 0
    if n==1:
      List.pop(0)
      List.pop(1)
      print(List)
    elif n==2:
      List.pop(0)
      print(List)
    else:
      for i in range(3,n+1): 
        List.append( List[List[i - 1]] + List[i - List[i - 1]]) 
      List.pop(0)
      print(List)

Initially a list List[] is created with values 0,1,1 in it.

And based on the value of n passed to it the contents in the list is printed.

If the value of n is less than or equal to 0 no output will be printed.

List.pop() function was used to remove the value 0 from the list List[] as this value was only added for calculations.

The screenshot of the code and the output generated is attached for your reference:

Hope it helps!!!